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Kelly worked on many other aspects of category theory besides enriched categories, both individually and in a number of collaborations. His PhD students include [[Ross Street]].
Kelly worked on many other aspects of category theory besides enriched categories, both individually and in a number of collaborations. His PhD students include [[Ross Street]].

==Selected publications==
{{Overdetailed|section|date=December 2020}}
The following annotated list of papers includes several papers not by Kelly which cover closely related work.

===Structures borne by categories===
* {{cite journal
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = Basic Concepts of Enriched Category Theory
| journal = Reprints in Theory and Applications of Categories
| volume = 10
| year = 2005
| origyear = 1982
| pages = 1–136
| url = http://tac.mta.ca/tac/reprints/articles/10/tr10abs.html
}} Originally published as [https://www.cambridge.org/core/series/london-mathematical-society-lecture-note-series London Mathematical Society Lecture Notes Series] '''64''' by [[Cambridge University Press]] in 1982. This book provides both a fundamental development of enriched category theory and, in the last two chapters, a study of generalized essentially algebraic theories in the enriched context. Chapters: 1. The elementary notions; 2. Functor categories; 3. Indexed [i.e., Weighted] limits and colimits; 4. Kan extensions; 5. Density; 6. Essentially-algebraic theories defined by reguli and by sketches.

Here are several of his papers on this subject. In the following "SLNM" stands for [https://link.springer.com/bookseries/304 Springer Lecture Notes in Mathematics], while the titles of the four journals most frequently publishing research on categories are abbreviated as follows: ''JPAA'' = [http://www.sciencedirect.com/science/journal/00224049 ''Journal of Pure and Applied Algebra''], ''TAC'' = [http://tac.mta.ca/tac/ ''Theory and Applications of Categories''], ''ACS'' = [https://link.springer.com/journal/10485 ''Applied Categorical Structures''], ''CTGDC'' = ''[[Cahiers de Topologie et Géométrie Différentielle Catégoriques]]'' (Volume XXV (1984) and later), ''CTGD'' = ''Cahiers de Topologie et Géométrie Différentielle'' (Volume XXIV (1983) and earlier). A website archiving both ''CTGD'' and ''CTGDC'' is [http://cahierstgdc.com/ here].

====Preliminaries====
* {{cite book
| last1 = Kelly
| first1 = G. M.
| author1-link = Max Kelly
| last2 = Street
| first2 = Ross
| author2-link = Ross Street
| title = Category Seminar (Proceedings Sydney Category Theory Seminar 1972/1973)
| chapter = Review of the elements of 2-categories
| series = SLNM
| volume = 420
| pages = 75–103
| date = 1974
| doi = 10.1007/BFb0063101 | isbn = 978-3-540-06966-9
}} "In §1 we rehearse the most elementary facts about [double categories and] 2-categories ... chiefly to introduce our notation and especially the operation of pasting that we use constantly. In §2 we use the pasting operation to give a treatment, which seems to us simpler and more complete than any we have seen, of the ['mates' bijection] <math>(bu,u'a) \cong (f'b,af)</math> arising from adjunctions <math>f \dashv u</math> and <math>f' \dashv u'</math> in any 2-category, and of its naturality. In §3 we recall the basic properties of monads in a 2-category, and then mention some enrichments of these that become available in the 2-category of 2-categories (because it is really a 3-category).". [https://golem.ph.utexas.edu/category/2014/03/review_of_the_elements_of_2cat.html Kan Extension Seminar discussion on 2014-03-09 by Dimitri Zaganidis]

====Some specific structures categories can bear====
* {{cite journal
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = Tensor products in categories
| journal = J. Algebra
| volume = 2
| pages = 15–37
| date = 1965
| doi = 10.1016/0021-8693(65)90022-0 }}

* {{cite book
| last1 = Eilenberg
| first1 = Samuel
| author1-link = Samuel Eilenberg
| last2 = Kelly
| first2 = G. Max
| author2-link = Max Kelly
| chapter = Closed categories
| title = Proceedings of the Conference on Categorical Algebra (La Jolla, 1965)
| pages = 421–562
| publisher = Springer-Verlag
| date = 1966
| isbn = 978-3-642-99902-4
| doi = 10.1007/978-3-642-99902-4_22 }}

* {{cite journal
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = A survey of totality for enriched and ordinary categories
| journal = CTGDC
| volume = 27
| issue = 2
| pages = 109–132
| date = 1986
| url = //www.numdam.org/item?id=CTGDC_1986__27_2_109_0
| mr = 850527
}}

* {{cite journal
| last1 = Im
| first1 = Geun Bin
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| title = A universal property of the convolution monoidal structure
| journal = JPAA
| volume = 43
| issue = 1
| pages = 75–88
| date = 1986
| doi = 10.1016/0022-4049(86)90005-8
}}

====Categories with few structures, or many====
* {{cite journal
| last1 = Foltz
| first1 = F.
| last2 = Lair
| first2 = C.
| last3 = Kelly
| first3 = G. M.
| author3-link = Max Kelly
| title = Algebraic categories with few monoidal biclosed structures or none
| journal = JPAA
| volume = 17
| issue = 2
| pages = 171–177
| date = 1980
| doi = 10.1016/0022-4049(80)90082-1 }}

* {{cite journal
| last1 = Kelly
| first1 = G. M.
| author1-link = Max Kelly
| last2 = Rossi
| first2 = F.
| title = Topological categories with many symmetric monoidal closed structures
| journal = Bull. Austral. Math. Soc.
| volume = 31
| issue = 1
| pages = 41–59
| date = 1985
| doi = 10.1017/S0004972700002264 | doi-access = free
}}

====Clubs====
* {{cite book
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = Coherence in Categories
| chapter = An abstract approach to coherence
| series = SLNM
| volume = 281
| pages= 106–147
| year = 1972
| doi = 10.1007/BFb0059557 | isbn = 978-3-540-05963-9
}} Mainly syntactic clubs, and how to present them. Closely related to the paper "Many-variable functorial calculus. I".

* {{cite book
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = Category Seminar (Proceedings Sydney Category Theory Seminar 1972/1973)
| chapter = On clubs and doctrines
| series = SLNM
| volume = 420
| pages = 181–256
| date = 1974
| doi = 10.1007/BFb0063104 | isbn = 978-3-540-06966-9
}}

* {{cite book
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = Applications of Categories in Computer Science (Proceedings of the London Mathematical Society Symposium, Durham 1991)
| chapter = On clubs and data-type constructors
| publisher = [[Cambridge University Press]]
| date = 1992
| pages = 163–190
| chapter-url = https://www.cambridge.org/core/books/applications-of-categories-in-computer-science/on-clubs-and-data-type-constructors/580CE981FECDC9B8B97EF43C8709E66A
| doi = 10.1017/CBO9780511525902.010 | isbn = 9780511525902
}} [https://golem.ph.utexas.edu/category/2017/04/on_clubs_and_datatype_construc.html Kan Extension Seminar discussion on 2017-04-17 by Pierre Cagne]

* {{cite journal
| last = Garner
| first = Richard
| title = Double clubs
| journal = CTGDC
| volume = 47
| issue = 4
| pages = 261–317
| date = 2006
| url = http://www.numdam.org/item/CTGDC_2006__47_4_261_0
| arxiv = math.CT/0606733
}}

====Coherence====
For an overview of Kelly's earlier and later views on coherence, see "An Abstract Approach to Coherence" (1972) and "On Clubs and Data-Type Constructors" (1992), listed in the section on clubs.

* {{cite journal
| last = Mac Lane
| first = Saunders
| author-link = Saunders Mac Lane
| title = Natural Associativity and Commutativity
| journal = Rice University Studies
| volume = 49
| issue = 4
| pages = 28–46
| date = 1963
| hdl = 1911/62865
}}

* {{cite journal
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = On MacLane's conditions for coherence of natural associativities, commutativities, etc.
| journal = J. Algebra
| volume = 1
| issue = 4
| pages = 397–402
| date = 1964
| doi = 10.1016/0021-8693(64)90018-3
}}

* {{cite journal
| last1 = Kelly
| first1 = G. M.
| author1-link = Max Kelly
| last2 = Mac Lane
| first2 = Saunders
| author2-link = Saunders Mac Lane
| title = Coherence in closed categories
| journal = JPAA
| volume = 1
| issue = 2
| pages = 97–140
| date = 1971
| doi = 10.1016/0022-4049(71)90013-2 }} : [http://www.sciencedirect.com/science/article/pii/0022404971900193 Erratum]

* {{cite book
| last1 = Kelly
| first1 = G. M.
| author1-link = Max Kelly
| last2 = Mac Lane
| first2 = Saunders
| author2-link = Saunders Mac Lane
| title = Coherence in Categories
| chapter = Closed coherence for a natural transformation
| series = SLNM
| volume = 281
| pages = 1–28
| date = 1972
| doi = 10.1007/BFb0059554 | isbn = 978-3-540-05963-9
}}

* {{cite book
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = Coherence in Categories
| chapter = A cut-elimination theorem
| series = SLNM
| volume = 281
| pages = 196–213
| date = 1972
| doi = 10.1007/BFb0059559
| isbn = 978-3-540-05963-9
}} Mainly a technical result needed for proving coherence results about closed categories, and more generally, about right adjoints.

* {{cite book
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = Category Seminar (Proceedings Sydney Category Theory Seminar 1972/1973)
| chapter = Coherence theorems for lax algebras and for distributive laws
| series = SLNM
| volume = 420
| pages = 281–375
| date = 1974
| doi = 10.1007/BFb0063106 | isbn = 978-3-540-06966-9
}} In this paper Kelly introduces the idea that coherence results may be viewed as equivalences, in a suitable 2-category, between pseudo and strict algebras.

* {{cite journal
| last1 = Kelly
| first1 = G. M.
| author1-link = Max Kelly
| last2 = LaPlaza
| first2 = M. L.
| title = Coherence for compact closed categories
| journal = JPAA
| volume = 19
| pages = 193–213
| date = 1980
| doi = 10.1016/0022-4049(80)90101-2 }}

* {{cite journal
| last = Power
| first = John
| title = A general coherence result
| journal = JPAA
| volume = 57
| issue = 2
| pages = 165–173
| date = 1989
| doi = 10.1016/0022-4049(89)90113-8
}}

* {{cite journal
| last = Lack
| first = Stephen
| title = Codescent objects and coherence (Dedicated to Max Kelly on the occasion of his 70th birthday)
| journal = JPAA
| volume = 175
| issue = 1
| pages = 223–241
| date = 1993
| doi = 10.1016/S0022-4049(02)00136-6
}} [https://golem.ph.utexas.edu/category/2014/06/codescent_objects_and_coherenc.html Kan Extension Seminar discussion on 2014-06-02 by Alex Corner]

====Lawvere theories, commutative theories, and the structure-semantics adjunction====

* {{cite journal
| last1 = Faro
| first1 = Emilio
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| title = On the canonical algebraic structure of a category
| journal = JPAA
| volume = 154
| issue = 1–3
| pages = 159–176
| date = 2000
| doi = 10.1016/S0022-4049(99)00187-5 }} For categories <math>A</math> satisfying some smallness conditions, "applying Lawvere's "structure" functor to the hom-functor <math>{\rm H} = {\rm Hom}_A : A^{\rm op} \times A \to {\rm Set}</math> produces a Lawvere theory <math>A^*</math>, called the ''canonical algebraic structure'' of <math>A</math>". --- In the first section, the authors "briefly recall the basic facts about Lawvere theories and the structure-semantics adjunction" before proceeding to apply it to the situation described above. The "brief" review runs over three pages in the printed journal. It may be the most complete exposition in print of how Kelly formulates, analyzes, and uses the notion of Lawvere theory.

====Local boundedness and presentability====
* {{cite journal
| last1 = Kelly
| first1 = G. M.
| author1-link = Max Kelly
| last2 = Lack
| first2 = Stephen
| title = <math>\cal V</math>-Cat is locally presentable or locally bounded if <math>\cal V</math> is so
| journal = TAC
| volume = 8
| issue = 23
| pages = 555–575
| date = 2001
| url = http://www.tac.mta.ca/tac/volumes/8/n23/8-23abs.html }}

====Monads====
* {{cite journal
| last = Street
| first = Ross
| author-link = Ross Street
| title = The formal theory of monads
| journal = JPAA
| volume = 2
| issue = 2
| pages = 149–168
| date = 1972
| doi = 10.1016/0022-4049(72)90019-9
| mr = 0299653
}} [https://golem.ph.utexas.edu/category/2014/01/formal_theory_of_monads_follow.html Kan Extension Seminar discussion on 2014-01-27 by Eduard Balzin]

* {{cite journal
| last1 = Blackwell
| first1 = R.
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| last3 = Power
| first3 = A. J.
| title = Two-dimensional monad theory
| journal = JPAA
| volume = 59
| issue = 1
| pages = 1–41
| date = 1989
| doi = 10.1016/0022-4049(89)90160-6 }} [https://golem.ph.utexas.edu/category/2014/04/on_two-dimensional_monad_theory.html Kan Extension Seminar discussion on 2014-04-28 by Sam van Gool]

====Monadicity====
* {{cite journal
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = Examples of non-monadic structures on categories
| journal = JPAA
| volume = 18
| issue = 1
| pages = 59–66
| date = 1980
| doi = 10.1016/0022-4049(80)90116-4 }}

* {{cite journal
| last1 = Kelly
| first1 = G. M.
| author1-link = Max Kelly
| last2 = Le Creurer
| first2 = I. J.
| title = On the monadicity over graphs of categories with limits
| journal = CTGDC
| volume = 38
| issue = 3
| pages = 179–191
| date = 1997
| url = http://www.numdam.org/item?id=CTGDC_1997__38_3_179_0
| mr = 1474564 }}

* {{cite journal
| last1 = Kelly
| first1 = G. M.
| author1-link = Max Kelly
| last2 = Lack
| first2 = Stephen
| title = On the monadicity of categories with chosen colimits
| journal = TAC
| volume = 7
| issue = 7
| pages = 148–170
| date = 2000
| url = http://tac.mta.ca/tac/volumes/7/n7/7-07abs.html }}

* {{cite journal
| last1 = Adamek
| first1 = Jiri
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| title = <math>\cal M</math>-Completeness is seldom monadic over graphs
| journal = TAC
| volume = 7
| issue = 8
| pages = 171–205
| date = 2000
| url = http://www.tac.mta.ca/tac/volumes/7/n8/7-08abs.html }}

====Operads====
* {{cite journal
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = On the operads of J.P. May
| journal = Reprints in Theory and Applications of Categories
| volume = 13
| pages = 1–13
| date = 2005
| origyear = 1972
| url = http://tac.mta.ca/tac/reprints/articles/13/tr13abs.html }} [https://golem.ph.utexas.edu/category/2017/03/on_the_operads_of_j_p_may.html Kan Extension Seminar discussion on 2017-03-01 by Simon Cho]

===Presentations===
* {{cite journal
| last1 = Dubuc
| first1 = Eduardo J.
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| title = A presentation of topoi as algebraic relative to categories or graphs
| journal = J. Algebra
| volume = 81
| issue = 2
| pages = 420–433
| date = 1983
| doi = 10.1016/0021-8693(83)90197-7 }}

* {{cite journal
| last1 = Kelly
| first1 = G. M.
| author1-link = Max Kelly
| last2 = Power
| first2 = A. J.
| title = Adjunctions whose counits are coequalizers, and presentations of finitary enriched monads
| journal = JPAA
| volume = 89
| issue = 1–2
| pages = 163–179
| date = 1993
| doi = 10.1016/0022-4049(93)90092-8 }} "Our primary goal is to show that - in the context of enriched category theory - every finitary monad on a locally finitely presentable category <math>\cal A</math> admits a presentation in terms of <math>\cal A</math>-objects Bc of 'basic operations of arity c' (where c runs through the finitely-presentable objects of <math>\cal A</math>) and <math>\cal A</math>-objects Ec of 'equations of arity c' between derived operations."—Section 4 is titled "Finitary enriched monads as algebras for finitary monads"; section 5 "Presentations of finitary monads"; it makes a connection with Lawvere theories.

* {{cite journal
| last1 = Kelly
| first1 = G. M.
| author1-link = Max Kelly
| last2 = Lack
| first2 = Stephen
| title = Finite-product-preserving functors, Kan extensions, and strongly-finitary 2-monads
| journal = ACS
| volume = 1
| issue = 1
| pages = 85–94
| date = 1993
| doi = 10.1007/BF00872987 }} Using the results in the Kelly-Power paper "Adjunctions whose counits are coequalizers, and presentations of finitary enriched monads" "We study those 2-monads on the 2-category '''Cat''' of categories which, as endofunctors, are the left Kan extensions of their restrictions to the sub-2-category of finite discrete categories, describing their algebras syntactically. Showing that endofunctors of this kind are closed under composition involves a lemma on left Kan extensions along a coproduct-preserving functor in the context of cartesian closed categories, which is closely related to an earlier result of Borceux and Day." --- in other words, they study "the subclass of the finitary 2-monads on '''Cat''' consisting of those whose algebras may be described using only functors <math>\cal A^n \to \cal A</math>, where <math>n</math> is a natural number (as well as natural transformations between these and equations between derived operations)". Cf. {{cite journal
| last = Street
| first = Ross
| author-link = Ross Street
| title = Kan extensions and cartesian monoidal categories
| journal = Seminarberichte der Mathematik
| volume = 87
| pages = 89–96
| date = 2015
| url = https://www.fernuni-hagen.de/mathinf/forschung/berichte_mathematik/berichte_2015.shtml
| arxiv = 1409.6405
| bibcode = 2014arXiv1409.6405S
}} "The existence of adjoints to algebraic functors between categories of models of Lawvere theories follows from finite-product-preservingness surviving left Kan extension. A result along these lines was proved in Appendix 2 of Brian Day's 1970 PhD thesis. His context was categories enriched in a cartesian closed base. A generalization is described here with essentially the same proof. We introduce the notion of cartesian monoidal category in the enriched context. With an advanced viewpoint, we give a result about left extension along a promonoidal module and further related results."

====Sketches, theories, and models====
For a presentation, in the unenriched setting, of some of the main ideas in the last half of ''BCECT'', see "On the Essentially-Algebraic Theory Generated by a Sketch". The first paragraph of the final section of that paper states an unenriched version of the final proclaimed theorem (6.23) of ''BCECT'', right down to the notation; the main body of the paper is devoted to the proof of that theorem in the unenriched context.

* {{cite journal
| last1 = Freyd
| first1 = P. J.
| author1-link = Peter J. Freyd
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| title = Categories of continuous functors, I
| journal = JPAA
| volume = 2
| issue = 3
| pages = 169–191
| date = 1972
| doi = 10.1016/0022-4049(72)90001-1
| mr = 0322004
}} : There is a very significant [http://www.sciencedirect.com/science/article/pii/0022404974900334 Erratum] ; [https://golem.ph.utexas.edu/category/2014/02/categories_of_continuous_funct.html Kan Extension Seminar discussion on 2014-02-15 by Fosco Loregian]

* {{cite journal
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = On the essentially-algebraic theory generated by a sketch
| journal = Bull. Austral. Math. Soc.
| volume = 26
| issue = 1
| pages = 45–56
| date = 1982
| url = https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/on-the-essentially-algebraic-theory-generated-by-a-sketch/2E08033166568856D3D19211C0D59D3D
| doi = 10.1017/S0004972700005591 | doi-access = free
}}

* {{cite journal
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = Structures defined by finite limits in the enriched context, I
| journal = CTGD
| volume = 23
| issue = 1
| pages = 3–42
| date = 1982
| url = http://www.numdam.org/item?id=CTGDC_1982__23_1_3_0
| mr = 648793 }} [https://golem.ph.utexas.edu/category/2017/04/enrichment_and_its_limits.html Kan Extension Seminar discussion of enriched, weighted limits on 2017-04-03 discussion of enriched, weighted limits by David Jaz Myers], followed by [https://golem.ph.utexas.edu/category/2017/04/gluing_together_finite_shapes.html 2017-04-03 discussion by the same commentator of other parts of the SFL article ]

====The property/structure distinction====
* {{cite journal
| last1 = Kelly
| first1 = G. M.
| author1-link = Max Kelly
| last2 = Lack
| first2 = Stephen
| title = On property-like structures
| journal = TAC
| volume = 3
| issue = 9
| pages = 213–250
| date = 1997
| url = http://tac.mta.ca/tac/volumes/1997/n9/3-09abs.html }} "we consider on a 2-category those 2-monads for which algebra structure is essentially unique if it exists, giving a precise mathematical definition of 'essentially unique' and investigating its consequences. We call such 2-monads ''property-like''. We further consider the more restricted class of ''fully property-like'' 2-monads, consisting of those property-like 2-monads for which all 2-cells between (even lax) algebra morphisms are algebra 2-cells. The consideration of lax morphisms leads us to a new characterization of those monads, studied by Kock and Zoberlein, for which 'structure is adjoint to unit', and which we now call ''lax-idempotent'' 2-monads: both these and their ''colax-idempotent'' duals are fully property-like. We end by showing that (at least for finitary 2-monads) the classes of property-likes, fully property-likes, and lax-idempotents are each coreflective among all 2-monads."

===Functor categories and functorial calculi===
Note that categories of sheaves and models are subcategories of functor categories, consisting of the functors which preserve certain structure. Here we consider the general case, functors only required to preserve the structure intrinsic to the source and target categories themselves.

* {{cite journal
| last1 = Eilenberg
| first1= Samuel
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| date = 1966
| title = A generalization of the functorial calculus
| journal = J. Algebra
| volume = 3
| issue = 3
| pages = 366–375
| doi = 10.1016/0021-8693(66)90006-8
| doi-access= free
}} Compare to Street "Functorial Calculus in Monoidal Bicategories" below.

* {{cite book
| last1 = Day
| first1 = B. J.
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| date = 1969
| chapter = Enriched functor categories
| title = Reports of the Midwest Category Seminar III
| series = SLNM
| volume = 106
| pages = 178–191
| doi = 10.1007/BFb0059146
| isbn = 978-3-540-04625-7
}}

* {{cite book
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = Coherence in Categories
| chapter = Many-variable functorial calculus. I.
| series = SLNM
| volume = 281
| pages=66–105
| year =1972
| doi =10.1007/BFb0059556 | isbn = 978-3-540-05963-9
}} Mainly semantic clubs. Closely related to the paper "An Abstract Approach to Coherence".

* {{cite journal
| last = Street
| first = Ross
| author-link = Ross Street
| title = Functorial Calculus in Monoidal Bicategories
| journal = ACS
| volume = 11
| issue = 3
| pages = 219–227
| date = 2003
| doi = 10.1023/A:1024247613677
}} "The definition and calculus of extraordinary natural transformations is extended to a context internal to any autonomous monoidal bicategory. The original calculus is recaptured from the geometry of the monoidal bicategory <math>\cal V{\bf -Mod}</math> whose objects are categories enriched in a cocomplete symmetric monoidal category <math>\cal V</math> and whose morphisms are modules." Compare to Eilenberg-Kelly "A generalization of the functorial calculus" above.

=== Bimodules, distributeurs, profunctors, proarrows, fibrations, and equipment ===
In several of his papers Kelly touched on the structures described in the heading. For the reader's convenience, and to enable easy comparisons, several closely related papers by other authors are included in the following list.

====Fibrations, cofibrations, and bimodules====
* {{cite book
| last = Gray
| first = John W.
| chapter = Fibred and Cofibred Categories
| title = Proceedings of the Conference on Categorical Algebra (La Jolla 1965)
| pages = 21–83
| date = 1966
| chapter-url = https://link.springer.com/book/10.1007/978-3-642-99902-4
| isbn = 978-3-642-99904-8
| doi = 10.1007/978-3-642-99902-4_2
}}

* {{cite book
| last = Street
| first = Ross
| author-link = Ross Street
| chapter = Fibrations and Yoneda's lemma in a 2-category
| title = Category Seminar (Proceedings Sydney Category Theory Seminar 1972/1973)
| series = SLNM
| volume = 420
| pages = 104–133
| date = 1974
| doi = 10.1007/BFb0063102
| mr = 0396723
| isbn = 978-3-540-06966-9
}} See also: {{cite arxiv
| last = Kock
| first = Anders
| title = Fibrations as Eilenberg-Moore algebras
| pages = 1–24
| date = 2013-12-05
| eprint = 1312.1608
| class = math.CT
}} Kock writes: "Street was probably the first to observe that opfibrations could be described as pseudo-algebras for a KZ monad [also known as [https://ncatlab.org/nlab/show/lax-idempotent+2-monad lax-idempotent 2-monad]]; in fact, in [F&YL], p. 118, he uses this description as his definition of the notion of opfibration, so therefore, no proof is given. Also, loc.cit. gives no proof of the fact that split opfibrations then are the strict algebras. So in this sense, Section 6 of the present article only supplements loc.cit. by providing elementary proofs of these facts."

* {{cite journal
| last = Street
| first = Ross
| author-link = Ross Street
| title = Fibrations in bicategories
| journal = CTGD
| volume = 21
| issue = 2
| pages = 111–160
| date = 1980
| url = http://www.numdam.org/item?id=CTGDC_1980__21_2_111_0
| mr = 574662 }}, followed in 1987 by a [http://www.numdam.org/item?id=CTGDC_1987__28_1_53_0 four page correction and addendum]. This paper discusses relations between <math>\cal V</math>-bimodules and two-sided fibrations and cofibrations in <math>\cal V</math>-Cat: "The <math>\cal V</math>-modules turn out to amount to the bicodiscrete cofibrations in <math>\cal V</math>-Cat." --- The paper by Kasangian, Kelly, and Rossi on cofibrations is closely related to these constructions.

* {{cite journal
| last1 = Kasangian
| first1 = S.
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| last3 = Rossi
| first3 = F.
| title = Cofibrations and the realization of non-deterministic automata
| journal = CTGD
| volume = 24
| issue = 1
| pages = 23–46
| date = 1983
| url = http://www.numdam.org/item?id=CTGDC_1983__24_1_23_0
| mr = 702718 }} Among other things, they develop the theory of bimodules over a biclosed, but not necessarily symmetric, monoidal category <math>\cal V</math>. Their development of the theory of cofibrations is modeled on that in Street's "Fibrations in bicategories."

* {{cite arxiv
| last = Streicher
| first = Thomas
| title = Fibred Categories à la Jean Bénabou
| pages =1–97
| date = 2018
| eprint = 1801.02927
| class = math.CT
}} "The notion of ''fibred category'' was introduced by A. Grothendieck for purely geometric reasons. The "logical" aspect of fibred categories and, in particular, their relevance for ''category theory over an arbitrary base category with pullbacks'' has been investigated and worked out in detail by Jean Bénabou. The aim of these notes is to explain Bénabou’s approach to fibred categories which is mostly unpublished but intrinsic to most fields of category theory, in particular to topos theory and categorical logic."

====Cosmoi====
* {{cite book
| last = Street
| first = Ross
| author-link = Ross Street
| chapter = Elementary cosmoi I
| title = Category Seminar (Proceedings Sydney Category Theory Seminar 1972/1973)
| series = SLNM
| volume = 420
| pages = 134–180
| date = 1974
| doi = 10.1007/BFb0063103
| mr = 0354813
| isbn = 978-3-540-06966-9
}}

* {{cite journal
| last = Street
| first = Ross
| author-link = Ross Street
| title = Cosmoi of internal categories
| journal = Trans. Amer. Math. Soc.
| volume = 258
| issue =2
| pages = 278–318
| date = 1980
| doi = 10.1090/S0002-9947-1980-0558176-3
| mr = 558176
| doi-access = free
}}

====Change of base and equipment====

* {{cite journal
| last = Wood
| first = R. J.
| author-link = Richard J. Wood
| title = Abstract proarrows I
| journal = CTGD
| volume = 23
| issue = 3
| pages = 279–290
| date = 1982
| url = //www.numdam.org/item?id=CTGDC_1982__23_3_279_0
| mr = 675339
}}

* {{cite journal
| last = Wood
| first = R. J.
| author-link = Richard J. Wood
| title = Proarrows II
| journal = CTGDC
| volume = 26
| issue = 2
| pages = 135–168
| date = 1985
| url = http://www.numdam.org/item?id=CTGDC_1985__26_2_135_0
| mr = 794752
}}

* {{cite journal
| last1 = Carboni
| first1 = A.
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| last3 = Wood
| first3 = R. J.
| author3-link = Richard J. Wood
| title = A 2-categorical approach to change of base and geometric morphisms I
| journal = CTGDC
| volume = 32
| issue = 1
| pages = 47–95
| date = 1991
| url = http://www.numdam.org/item?id=CTGDC_1991__32_1_47_0
| mr = 1130402 }}

* {{cite journal
| last1 = Carboni
| first1 = A.
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| last3 = Verity
| first3 = D.
| last4 = Wood
| first4 = R. J.
| author4-link = Richard J. Wood
| title = A 2-Categorical Approach To Change of Base And Geometric Morphisms II
| journal = TAC
| volume = 4
| issue = 5
| pages = 82–136
| date = 1998
| url = http://www.tac.mta.ca/tac/volumes/1998/n5/4-05abs.html }} "We introduce a notion of ''equipment'' which generalizes the earlier notion of ''pro-arrow equipment'' and includes such familiar constructs as '''rel'''<math>\cal K</math>, '''spn'''<math>\cal K</math>, '''par'''<math>\cal K</math>, and '''pro'''<math>\cal K</math> for a suitable category <math>\cal K</math>, along with related constructs such as the <math>\cal V</math>-'''pro''' arising from a suitable monoidal category <math>\cal V</math>."

* {{cite journal
| last = Shulman
| first = Michael
| author-link = Michael Shulman (mathematician)
| title = Framed bicategories and monoidal fibrations
| journal = TAC
| volume = 20
| issue = 18
| pages = 650–738
| date = 2008
| url = http://www.tac.mta.ca/tac/volumes/20/18/20-18abs.html
}} This paper generalizes the notion of equipment. The author writes: "The authors of [CKW91, CKVW98] consider a related notion of 'equipment' where <math>K</math> is replaced by a 1-category but the horizontal composition is forgotten." In particular, one of his constructions yields what [CKVW98] calls a ''starred pointed equipment''.

* {{cite journal
| last = Verity
| first = Dominic
| title = Enriched categories, internal categories and change of base
| journal = Reprints in Theory and Applications of Categories
| volume = 20
| year = 2011
| origyear = 1992
| pages = 1–266
| url = http://tac.mta.ca/tac/reprints/articles/20/tr20abs.html
}} "[C]hapter 1 presents a general theory of change of base for category theories as codified into structures called equipments. These provide an abstract framework which combines the calculi of functors and profunctors of a given category theory into a single axiomatised structure, in a way which applies to enriched and internal theories alike."

* {{cite journal
| last1 = Street
| first1 = Ross
| author1-link = Ross Street
| last2 = Walters
| first2 = Robert
| title = Yoneda structures on 2-categories
| journal = J. Algebra
| volume = 50
| issue = 2
| pages = 360–379
| date = 1978
| doi = 10.1016/0021-8693(78)90160-6
| mr = 0463261
}}, [https://golem.ph.utexas.edu/category/2014/03/an_exegesis_of_yoneda_structur.html Kan Extension Seminar discussion on 2014-03-24 by Alexander Campbell]

* {{cite journal
| last1 = Carboni
| first1 = A.
| last2 = Walters
| first2 = R. F. C.
| title = Cartesian bicategories I
| journal = JPAA
| volume = 49
| issue = 1–2
| pages = 11–32
| date = 1987
| doi = 10.1016/0022-4049(87)90121-6 }}

* {{cite journal
| last1 = Carboni
| first1 = A.
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| last3 = Walters
| first3 = R. F. C.
| last4 = Wood
| first4 = R. J.
| author4-link = Richard J. Wood
| title = Cartesian bicategories II
| journal = TAC
| volume = 19
| issue = 6
| pages = 93–124
| date = 2008
| url = http://www.tac.mta.ca/tac/volumes/19/6/19-06abs.html
| arxiv = 0708.1921
| bibcode = 2007arXiv0708.1921C
}} "The notion of ''cartesian bicategory'', introduced by Carboni and Walters for locally ordered bicategories, is extended to general bicategories. It is shown that a cartesian bicategory is a symmetric monoidal bicategory."

===Factorization systems, reflective subcategories, localizations, and Galois theory===
* {{cite journal
| last = Kelly
| first = G.M.
| author-link = Max Kelly
| title = Monomorphisms, Epimorphisms, and Pull-Backs
| journal = J. Austral. Math. Soc.
| volume = 9
| issue = 1–2
| pages = 124–142
| date = 1969
| doi = 10.1017/S1446788700005693 | doi-access = free
}}

* {{cite journal
| last = Kelly
| first = G.M.
| author-link = Max Kelly
| title = A note on the generalized reflexion of Guitart and Lair
| journal = CTGD
| volume = 24
| issue = 2
| pages = 155–159
| date = 1983
| url = http://www.numdam.org/item?id=CTGDC_1983__24_2_155_0
| mr = 710038 }}

* {{cite journal
| last1 = Cassidy
| first1 = C.
| last2 = Hébert
| first2 = M.
| last3 = Kelly
| first3 = G. M.
| author-link3 = Max Kelly
| title = Reflective subcategories, localizations and factorization systems
| journal = J. Austral. Math. Soc.
| volume = 38
| issue = 3
| pages = 287–329
| date = 1985
| doi = 10.1017/S1446788700023624 | doi-access = free
}}, followed by [https://www.cambridge.org/core/journals/journal-of-the-australian-mathematical-society/article/reflective-subcategories-localizations-and-factorization-systems-corrigenda/AAC3AC8105F62B74BBE37C4BED78E68F Corrigenda]. "This work is a detailed analysis of the relationship between reflective subcategories of a category and factorization systems supported by the category."

* {{cite journal
| last1 = Borceux
| first1 = F.
| last2 = Kelly
| first2 = G.M.
| author2-link = Max Kelly
| title = On locales of localizations
| journal = JPAA
| volume = 46
| issue = 1
| pages = 1–34
| date = 1987
| doi=10.1016/0022-4049(87)90040-5}} "Our aim is to study the ordered set Loc <math>\cal A</math> of localizations of a category <math>\cal A</math>, showing it to be a small complete lattice when <math>\cal A</math> is complete with a (small) strong generator, and further to be the dual of a locale when <math>\cal A</math> is a locally-presentable category in which finite limits commute with filtered colimits. We also consider the relations between Loc <math>\cal A</math> and Loc <math>\cal A'</math> arising from a geometric morphism <math>\cal A</math> → <math>\cal A'</math>; and apply our results in particular to categories of modules."

* {{cite journal
| last = Kelly
| first = G.M.
| author-link = Max Kelly
| title = On the ordered set of reflective subcategories
| journal = Bull. Austral. Math. Soc.
| volume = 36
| issue = 1
| pages = 137–152
| date = 1987
| url = https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/div-classtitleon-the-ordered-set-of-reflective-subcategoriesdiv/454DDBE1FF26905053E758B9F9C20812
| doi = 10.1017/S0004972700026381 | doi-access = free
}} "Given a category <math>\cal A</math>, we consider the (often large) set Ref <math>\cal A</math> of its reflective (full, replete) subcategories, ordered by inclusion."

* {{cite journal
| last1 = Kelly
| first1 = G.M.
| author1-link = Max Kelly
| last2 = Lawvere
| first2 = F.W.
| author2-link = William Lawvere
| title = On the Complete Lattice of Essential Localizations
| journal = Bulletin de la Société Mathématique de Belgique Series A
| volume = 41
| pages = 289–319
| date = 1989 }} No copy of this could be found on the web as of 2017-09-29.

* {{cite book
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| chapter = A note on relations relative to a factorization system
| title = Proceedings of the International Conference held in Como, Italy, July 22–28, 1990
| series = SLNM
| volume = 1488
| pages = 249–261
| date = 1991
| doi = 10.1007/BFb0084224 | isbn = 978-3-540-54706-8
}}

*{{cite journal
| last1 = Korostenski
| first1 = Mareli
| last2 = Tholen
| first2 = Walter
| title = Factorization systems as Eilenberg-Moore algebras
| journal = JPAA
| volume = 85
| issue = 1
| pages = 57–72
| date = 1993
| doi = 10.1016/0022-4049(93)90171-O
}}

* {{cite journal
| last1 = Carboni
| first1 = A.
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| last3 = Pedicchio
| first3 = M. C.
| title = Some remarks on Maltsev and Goursat categories
| journal = ACS
| volume = 1
| issue = 4
| pages = 385–421
| date = 1993
| doi = 10.1007/BF00872942 }} : Begins with basic treatment of ''regular'' and ''exact'' categories, and equivalence relations and congruences therein, then studies the Maltsev and Goursat conditions.

* {{cite journal
| last1 = Janelidze
| first1 = G.
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| title = Galois theory and a general notion of central extension
| journal = JPAA
| volume = 97
| issue = 2
| pages = 135–161
| date = 1994
| doi = 10.1016/0022-4049(94)90057-4 }} "We propose a theory of ''central extensions'' for universal algebras, and more generally for objects in an exact category <math>\cal C</math>, centrality being defined relatively to an "admissible" full subcategory <math>\cal X</math> of <math>\cal C</math>."

* {{cite journal
| last1 = Carboni
| first1 = A.
| last2 = Janelidze
| first2 = G.
| last3 = Kelly
| first3 = G. M.
| author3-link = Max Kelly
| last4 = Paré
| first4 = R.
| title = On Localization and Stabilization for Factorization Systems
| journal = ACS
| volume = 5
| issue = 1
| pages = 1–58
| date = 1997
| doi = 10.1023/A:1008620404444 }} : includes "self-contained modern accounts of factorization systems, descent theory, and Galois theory"

* {{cite journal
| last1 = Janelidze
| first1 = G.
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| title = The reflectiveness of covering morphisms in algebra and geometry
| journal = TAC
| volume = 3
| issue = 6
| pages = 132–159
| date = 1997
| url = http://tac.mta.ca/tac/volumes/1997/n6/3-06abs.html }} "Many questions in mathematics can be reduced to asking whether Cov(B) is reflective in C \downarrow B; and we give a number of disparate conditions, each sufficient for this to be so."

* {{cite journal
| last1 = Janelidze
| first1 = G.
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| title = Central extensions in universal algebra: a unification of three notions
| journal = Algebra Universalis
| volume = 44
| issue = 1–2
| pages = 123–128
| date = 2000
| doi = 10.1007/s000120050174
}}

* {{cite journal
| last1 = Rosebrugh
| first1 = Robert
| last2 = Wood
| first2 = R. J.
| author2-link = Richard J. Wood
| title = Distributive laws and factorization
| journal = JPAA
| volume = 175
| issue = 1–3
| pages = 327–353
| date = 2001
| doi = 10.1016/S0022-4049(02)00140-8
}}

===Actions and algebras===
Also semidirect products.
* {{cite journal
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = A unified treatment of transfinite constructions for free algebras, free monoids, colimits, associated sheaves, and so on
| journal = Bull. Austral. Math. Soc.
| volume = 22
| issue = 1
| pages = 1–83
| date = 1980
| doi = 10.1017/S0004972700006353 | doi-access = free
}}, followed by: [https://www.cambridge.org/core/journals/bulletin-of-the-australian-mathematical-society/article/two-addenda-to-the-authors-transfinite-constructions/ACD6B09DD2FC923B8ECC15DCD876688E "Two addenda to the author's ‘Transfinite constructions’ "]

* {{cite journal
| last1 = Janelidze
| first1 = G.
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| title = A Note on Actions of a Monoidal Category
| journal = TAC
| volume = 9
| issue = 4
| pages = 61–91
| date = 2001
| url = http://www.tac.mta.ca/tac/volumes/9/n4/9-04abs.html }}

* {{cite journal
| last1 = Borceux
| first1 = F.W.
| last2 = Janelidze
| first2 = G.
| last3 = Kelly
| first3 = G.M.
| author3-link = Max Kelly
| title = On the representability of actions in a semi-abelian category
| journal = TAC
| volume = 14
| issue = 11
| pages = 244–286
| date = 2005
| url = http://tac.mta.ca/tac/volumes/14/11/14-11abs.html }} "We consider a semi-abelian category <math>\cal V</math> and we write Act(G,X) for the set of actions of the object G on the object X, in the sense of the theory of semi-direct products in <math>\cal V</math>. We investigate the representability of the functor Act(-,X) in the case where <math>\cal V</math> is locally presentable, with finite limits commuting with filtered colimits."

* {{cite journal
| last1 = Borceux
| first1 = Francis
| last2 = Janelidze
| first2 = George W.
| last3 = Kelly
| first3 = Gregory Maxwell
| author3-link = Max Kelly
| title = Internal object actions
| journal = Commentationes Mathematicae Universitatis Carolinae
| volume = 46
| issue = 2
| pages = 235–255
| date = 2005
| url = https://eudml.org/doc/249553
| mr = 2176890 }} "We describe the place, among other known categorical constructions, of the internal object actions involved in the categorical notion of semidirect product, and introduce a new notion of representable action providing a common categorical description for the automorphism group of a group, for the algebra of derivations of a Lie algebra, and for the actor of a crossed module." --- Contains a table showing various examples.

===Limits and colimits===
* {{cite journal
| last1 = Borceux
| first1 = Francis
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| date = 1975
| title = A notion of limit for enriched categories
| journal = Bull. Austral. Math. Soc.
| volume = 12
| issue = 1
| pages = 49–72
| doi = 10.1017/S0004972700023637
| doi-access= free
}}

* {{cite journal
| last1 = Kelly
| first1 = G. M.
| author1-link = Max Kelly
| last2 = Koubek
| first2 = V.
| date = 1981
| title = The large limits that all good categories admit
| journal = JPAA
| volume = 22
| issue = 3
| pages = 253–263
| doi = 10.1016/0022-4049(81)90102-X
}}

* {{cite journal
| last1 = Im
| first1 = Geun Bin
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| date = 1986
| title = On classes of morphisms closed under limits
| url = http://basilo.kaist.ac.kr/mathnet/thesis_file/JKMS-23-1-1-18.pdf
| journal = J. Korean Math. Soc.
| volume = 23
| issue = 1
| pages = 1–18
}} "We say that a class <math>\cal M</math> of morphisms in a category <math>\cal A</math> is ''closed under limits'' if, whenever <math>F, G : \cal K \to \cal A</math> are functors that admit limits, and whenever <math>\eta : F \Rightarrow G : \cal K \to \cal A</math> is a natural transformation each of whose components <math>\eta K : FK \to GK</math> lies in <math>\cal M</math>, then the induced morphism <math>{\rm lim}~\eta : {\rm lim}~F \to {\rm lim}~G</math> also lies in <math>\cal M</math>."

* {{cite journal
| last1 = Albert
| first1 = M. H.
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| date = 1988
| title = The closure of a class of colimits
| journal = JPAA
| volume = 51
| issue = 1–2
| pages = 1–17
| doi = 10.1016/0022-4049(88)90073-4
}}

* {{cite journal
| last1 = Kelly
| first1 = G. M.
| author1-link = Max Kelly
| last2 = Paré
| first2 = Robert
| date = 1988
| title = A note on the Albert–Kelly paper "the closure of a class of colimits"
| journal = JPAA
| volume = 51
| issue = 1–2
| pages = 19–25
| doi = 10.1016/0022-4049(88)90074-6
}}

* {{cite journal
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = Elementary observations on 2-categorical limits
| journal = Bull. Austral. Math. Soc.
| volume = 39
| issue = 2
| pages = 301–317
| date = 1989
| doi = 10.1017/S0004972700002781
| doi-access = free
}} [https://golem.ph.utexas.edu/category/2014/04/elementary_observations_on_2ca.html Kan Extension Seminar discussion on 2014-04-18 by Christina Vasilakopoulou]

* {{cite journal
| last1 = Bird
| first1 = G. J.
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| last3 = Power
| first3 = A. J.
| last4 = Street
| first4 = R. H.
| author4-link = Ross Street
| title = Flexible limits for 2-categories
| journal = JPAA
| volume = 61
| issue = 1
| pages = 1–27
| date = 1989
| doi = 10.1016/0022-4049(89)90065-0
}}

* {{cite journal
| last1 = Kelly
| first1 = G. M.
| author1-link = Max Kelly
| last2 = Lack
| first2 = Stephen
| last3 = Walters
| first3 = R. F. C.
| title = Coinverters and categories of fractions for categories with structure
| journal = ACS
| volume = 1
| issue = 1
| pages = 95–102
| date = 1993
| doi = 10.1007/BF00872988 }} "A category of fractions is a special case of a ''coinverter'' in the 2-category '''Cat'''...."

* {{cite journal
| last1 = Kelly
| first1 = G. M.
| author1-link = Max Kelly
| last2 = Schmitt
| first2 = V.
| title = Notes on enriched categories with colimits of some class
| journal = TAC
| volume = 14
| issue = 17
| pages = 399–423
| date = 2005
| url = http://www.tac.mta.ca/tac/volumes/14/17/14-17abs.html
| arxiv = math.CT/0509102
}} "The paper is in essence a survey of categories having <math>\phi</math>-weighted colimits for all the weights <math>\phi</math> in some class <math>\Phi</math>."

===Adjunctions===
* {{cite book
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = Reports of the Midwest Category Seminar III
| series = SLNM
| volume = 106
| pages = 166–177
| date = 1969
| chapter = Adjunction for enriched categories
| doi = 10.1007/BFb0059145
| isbn = 978-3-540-04625-7
}}

* {{cite book
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| chapter = Doctrinal adjunction
| title = Category Seminar (Proceedings Sydney Category Theory Seminar 1972/1973)
| series = SLNM
| volume = 420
| pages = 257–280
| date = 1974
| doi = 10.1007/BFb0063105
| isbn = 978-3-540-06966-9
}}

* {{cite journal
| last1 = Im
| first1= Geun Bin
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| title = Some remarks on conservative functors with left adjoints
| journal = J. Korean Math. Soc.
| volume = 23
| issue = 1
| pages = 19–33
| date = 1986
| url = http://icms.kaist.ac.kr/mathnet/thesis_file/JKMS-23-1-19-33.pdf
}} "We are interested here in those functors which, like the forgetful functors of algebra, are conservative and have left adjoints."

* {{cite journal
| last1 = Im
| first1 = Geun Bin
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| title = Adjoint-triangle theorems for conservative functors
| journal = Bull. Austral. Math. Soc.
| volume = 36
| issue = 1
| pages = 133–136
| date = 1987
| doi = 10.1017/S000497270002637X
| doi-access = free
}} "An ''adjoint-triangle theorem'' contemplates functors <math>P: \cal C \to \cal A</math> and <math>T: \cal A \to \cal B</math> where <math>T</math> and <math>TP</math> have left adjoints, and gives sufficient conditions for <math>P</math> also to have a left adjoint. We are concerned with the case where <math>T</math> is ''conservative'' - that is, isomorphism-reflecting"

* {{cite journal
| last1 = Kelly
| first1 = G. M.
| author1-link = Max Kelly
| last2 = Power
| first2 = A. J.
| title = Adjunctions whose counits are coequalizers, and presentations of finitary enriched monads
| journal = JPAA
| volume = 89
| issue = 1–2
| pages = 163–179
| date = 1993
| doi = 10.1016/0022-4049(93)90092-8
}} This is a duplicate of a reference in the section on structures borne by categories, which is the subject of the last two sections of the paper. However the first three sections are about "functors of ''descent type'' ", which are right adjoint functors enjoying the property stated in the title of the paper.

* {{cite journal
| last = Street
| first = Ross
| author-link = Ross Street
| title = The core of adjoint functors
| journal = TAC
| volume = 27
| issue = 4
| pages = 47–64
| date = 2012
| url = http://tac.mta.ca/tac/volumes/27/4/27-04abs.html
}} "There is a lot of redundancy in the usual definition of adjoint functors. We define and prove the core of what is required. First we do this in the hom-enriched context. Then we do it in the cocompletion of a bicategory with respect to Kleisli objects, which we then apply to internal categories. Finally, we describe a doctrinal setting."

===Miscellaneous papers on category theory===
* {{cite journal
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = On the radical of a category
| journal = J. Austral. Math. Soc.
| volume = 4
| issue = 3
| pages = 299–307
| date = 1964
| doi = 10.1017/S1446788700024071
| doi-access = free
}}

* {{cite journal
| last1 = Day
| first1 = B. J.
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| title = On topological quotient maps preserved by pullbacks or products
| journal = Math. Proc. Camb. Phil. Soc.
| volume = 67
| issue = 3
| pages = 553
| date = 1970
| doi = 10.1017/S0305004100045850
| bibcode = 1970PCPS...67..553D
}} This paper is in the intersection of category theory and topology: "We are concerned with the category of topological spaces and continuous maps." It is mentioned in ''BCECT'', where it provides a counter-example to the conjecture that the cartesian monoidal category <math>\bf Top</math> of topological spaces might be cartesian closed; see section 1.5.

* {{cite book
| editor1-last = Kelly
| editor1-first = G. M.
| editor1-link = Max Kelly
| editor2-last = Street
| editor2-first = Ross
| editor2-link = Ross Street
| title = Abstracts of the Sydney Category Seminar 1972
| pages = 1–66
| date = 1972
| url = http://maths.mq.edu.au/~street/Christmas1972.pdf
}} Some historical information on personnel matters, and early versions of ideas to be published formally later.

* {{cite journal
| last1 = Kelly
| first1 = Max
| author1-link = Max Kelly
| last2 = Labella
| first2 = Anna
| last3 = Schmitt
| first3 = Vincent
| last4 = Street
| first4 = Ross
| author4-link = Ross Street
| date = 2002
| title = Categories enriched on two sides (Dedicated to Saunders Mac Lane on his 90th birthday)
| journal = JPAA
| volume = 168
| issue = 1
| pages = 53–98
| doi = 10.1016/S0022-4049(01)00048-2
}}

* {{cite journal
| last1 = Kelly
| first1 = G. M.
| author1-link = Max Kelly
| last2 = Lack
| first2 = Stephen
| title = Monoidal functors generated by adjunction, with applications to transport of structure
| journal = Fields Institute Communications
| volume = 43
| pages = 319–340
| date = 2004
| url = http://maths.mq.edu.au/~slack/papers/transport.html
| issn = 1069-5265
}}
* {{cite book
| last1 = Kelly
| first1 = G. Maxwell
| author1-link = Max Kelly
| title = Categories in Algebra, Geometry and Mathematical Physics
| chapter = The beginnings of category theory in Australia.
| series = Contemporary Math.
| volume = 431
| pages = 1–6
| date = 2007
| publisher = Amer. Math. Soc.
| chapter-url = http://bookstore.ams.org/conm-431
| isbn = 978-0-8218-3970-6
}} A historical account.

===Homology===
The [https://www.science.org.au/fellowship/fellows/biographical-memoirs/gregory-maxwell-kelly-1930%E2%80%932007 Biographical Memoir] by Ross Street gives a detailed description of Kelly's early research on homological algebra,
pointing out how it led him to create concepts which would eventually be given the names "[https://ncatlab.org/nlab/show/dg-category differential graded categories]" and "[https://ncatlab.org/nlab/show/anafunctor anafunctors]".
* {{cite journal
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = Single-space axioms for homology theory
| journal = Mathematical Proceedings of the Cambridge Philosophical Society
| volume = 55
| issue = 1
| pages = 10–22
| date = 1959
| doi = 10.1017/S030500410003365X
| bibcode = 1959PCPS...55...10K
}}

* {{cite journal
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = The exactness of Čech homology over a vector space
| journal = Math. Proc. Camb. Phil. Soc.
| volume = 57
| issue = 2
| pages = 428–429
| date = 1961
| doi = 10.1017/S0305004100035398
| bibcode = 1961PCPS...57..428K
}}

* {{cite journal
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = On manifolds containing a submanifold whose complement is contractible
| journal = Math. Proc. Camb. Phil. Soc.
| volume = 57
| issue = 3
| pages = 507–515
| date = 1961
| doi = 10.1017/S0305004100035568
| bibcode = 1961PCPS...57..507K
}}

* {{cite journal
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = Observations on the Künneth theorem
| journal = Math. Proc. Camb. Phil. Soc.
| volume = 59
| issue = 3
| pages = 575–587
| date = 1963
| doi = 10.1017/S0305004100037257
| bibcode = 1963PCPS...59..575K
}}

* {{cite journal
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = Complete functors in homology I. Chain maps and endomorphisms
| journal = Math. Proc. Camb. Phil. Soc.
| volume = 60
| issue = 4
| pages = 721–735
| date = 1964
| doi = 10.1017/S0305004100038202
| bibcode = 1964PCPS...60..721K
}}

* {{cite journal
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = Complete functors in Homology: II. The exact homology sequence
| journal = Math. Proc. Camb. Phil. Soc.
| volume = 60
| issue = 4
| pages = 737–749
| date = 1964
| doi = 10.1017/S0305004100038214
| bibcode = 1964PCPS...60..737K
}}

* {{cite journal
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = A lemma in homological algebra
| journal = Math. Proc. Camb. Phil. Soc.
| volume = 61
| issue = 1
| pages = 49–52
| date = 1965
| doi = 10.1017/S0305004100038627
| bibcode = 1965PCPS...61...49K
}}

* {{cite journal
| last = Kelly
| first = G. M.
| author-link = Max Kelly
| title = Chain maps inducing zero homology maps
| journal = Math. Proc. Camb. Phil. Soc.
| volume = 61
| issue = 4
| pages = 847–854
| date = 1965
| doi = 10.1017/S0305004100039207
| bibcode = 1965PCPS...61..847K
}}

===Miscellaneous papers on other subjects===
* {{cite journal
| last1 = Dickson
| first1 = S. E.
| last2 = Kelly
| first2 = G. M.
| author2-link = Max Kelly
| title = Interlacing methods and large indecomposables
| journal = Bull. Austral. Math. Soc.
| volume = 3
| issue = 3
| pages = 337–348
| date = 1970
| doi = 10.1017/S0004972700046037
| doi-access = free
}}

* {{cite journal
| last1 = Kelly
| first1 = G. M.
| author1-link = Max Kelly
| last2 = Pultr
| first2 = A.
| title = On algebraic recognition of direct-product decompositions
| journal = JPAA
| volume = 12
| issue = 3
| pages = 207–224
| date = 1978
| doi = 10.1016/0022-4049(87)90002-8
}}

=== General references ===
* {{cite journal
| last1 = Carboni | first1 = Aurelio
| last2 = Janelidze | first2 = George
| last3 = Street | first3 = Ross
| author3-link = Ross Street
| title = Forward to Special Volume Celebrating the 70th Birthday of Professor Max Kelly
| journal = [[Journal of Pure and Applied Algebra]]
| volume = 175
| issue = 1–3
| pages = 1–5
| date = 8 November 2002
| doi = 10.1016/S0022-4049(02)00125-1 }} : contains list of 87 publications of Kelly from 1959 to early 2002

* {{cite news
| last = Street
| first = Ross
| author-link = Ross Street
| title = Obituary : Polymath revelled in the mystery of numbers
| newspaper = Sydney Morning Herald
| date = 11 April 2007
| url = http://www.smh.com.au/news/obituaries/polymath-revelled-in-the-mystery-of-numbers/2007/04/10/1175971094331.html
| access-date = 2017-09-08 }}
* {{cite journal
| last = Street | first = Ross
| author-link = Ross Street
| title = Editorial Notice: Max Kelly 5 June 1930 - 26 January 2007
| journal = Theory and Applications of Categories
| volume = 20
| pages = 1–4
| date = 2008
| url = http://tac.mta.ca/tac/volumes/20/notice/20-notice.pdf }}
* {{Cite web
| url = https://www.science.org.au/fellowship/fellows/biographical-memoirs/gregory-maxwell-kelly-1930%E2%80%932007
| title = Biographical Memoir : Gregory Maxwell Kelly 1930–2007
| last = Street
| first = Ross
| author-link = Ross Street
| year = 2010
| publisher = Australian Academy of Sciences
}} : includes complete list of 92 publications from 1957 PhD thesis to posthumously published 2008 paper ; probably the most complete survey of Kelly’s career
* {{cite book
| editor1-last = Baez | editor1-first = John C.
| editor1-link = John C. Baez
| editor2-last = May | editor2-first = J. Peter
| editor2-link = J. Peter May
| title = Towards Higher Categories
| publisher = [[Springer-Verlag]]
| series = The IMA Volumes in Mathematics and its Applications
| volume = 152
| date = 2010
| doi = 10.1007/978-1-4419-1524-5
| isbn = 978-1-4419-1523-8
}} : "This book is dedicated to Max Kelly, the founder of the Australian school of category theory"

* {{cite book
| last = Street
| first = Ross
| author-link = Ross Street
| chapter = An Australian Conspectus of Higher Categories
| pages = 237–264
| editor1-last = Baez | editor1-first = J.
| editor1-link = John C. Baez
| editor2-last = May | editor2-first = J.
| editor2-link = J. Peter May
| title = Towards Higher Categories
| publisher = [[Springer-Verlag]]
| series = The IMA Volumes in Mathematics and its Applications
| volume = 152
| date = 2010
| chapter-url = https://link.springer.com/book/10.1007/978-1-4419-1524-5
| doi = 10.1007/978-1-4419-1524-5_6
| isbn = 978-1-4419-1523-8
}} From the forward to the book: "[This paper], by Kelly’s student Ross Street, gives a fascinating mathematical and personal account of the development of higher category theory in Australia." The first quarter of the article contains information about the work of Kelly. It is available from the author [http://maths.mq.edu.au/~street/Minneapolis.pdf here].

* {{cite journal
| editor1-last = Janelidze | editor1-first = George
| editor2-last = Hyland | editor2-first = Martin
| editor2-link = Martin Hyland
| editor3-last = Johnson | editor3-first = Michael|display-editors=etal
| title = Forward to Special Issue Dedicated to the Memory of Professor Gregory Maxwell Kelly
| journal = Applied Categorical Structures
| volume = 19
| issue = 1
| pages = 1–7
| date = February 2011
| doi = 10.1007/s10485-010-9235-y }} : contains list of publications of Kelly


== External links ==
== External links ==

Revision as of 20:33, 21 December 2020

For the Australian rules footballer, see Max Kelly (footballer).

Gregory Maxwell Kelly
Born5 June 1930
Died26 January 2007
Alma materUniversity of Cambridge
Known forEnriched category theory
AwardsCentenary Medal
Scientific career
FieldsMathematics
InstitutionsUniversity of Sydney
Thesis Topics in Homology Theory  (1957)
Doctoral advisorShaun Wylie
Doctoral studentsRoss Street

Gregory Maxwell "Max" Kelly (5 June 1930 – 26 January 2007) is a mathematician who worked on category theory.

Biography

A native of Australia, Kelly obtained his PhD at Cambridge University in homological algebra in 1957, publishing his first paper in that area in 1959, Single-space axioms for homology theory. He taught in the Pure Mathematics department at Sydney University from 1957 to 1966, rising from lecturer to reader. During 1963–1965 he was a visiting fellow at Tulane University and the University of Illinois, where with Samuel Eilenberg he formalized and developed the notion of an enriched category based on intuitions then in the air about making the homsets of a category just as abstract as the objects themselves.

He subsequently developed the notion in considerably more detail in his 1982 monograph Basic Concepts of Enriched Category Theory (henceforth abbreviated BCECT). Let be a monoidal category, and denote by -Cat the category of -enriched categories. Among other things, Kelly showed that -Cat has all weighted limits and colimits even when does not have all ordinary limits and colimits. He also developed the enriched counterparts of Kan extensions, density of the Yoneda embedding, and essentially algebraic theories.

In 1967 Kelly was appointed Professor of Pure Mathematics at the University of New South Wales. In 1972 he was elected a Fellow of the Australian Academy of Science. He returned to the University of Sydney in 1973, serving as Professor of Mathematics until his retirement in 1994. In 2001 he was awarded the Australian government's Centenary Medal. He continued to participate in the department as professorial fellow and professor emeritus until his death at age 76 on 26 January 2007.

Kelly worked on many other aspects of category theory besides enriched categories, both individually and in a number of collaborations. His PhD students include Ross Street.

  • O'Connor, John J.; Robertson, Edmund F., "Max Kelly", MacTutor History of Mathematics Archive, University of St Andrews
  • Gregory Maxwell (Max) Kelly at the Mathematics Genealogy Project Edit this at Wikidata
  • Max Kelly's Perpetual Web Page: a memorial page set up by Kelly's son Simon Kelly.
  • "In Memory of Max Kelly": a post at The n-Category Café, containing praise from his fellow mathematicians
  • G. M. Kelly at DBLP Bibliography Server Edit this at Wikidata
Retrieved from "https://en.wikipedia.org/w/index.php?title=Max_Kelly&oldid=995578133"