Max Kelly

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

Gregory Maxwell Kelly
Born	5 June 1930
Died	26 January 2007
Alma mater	University of Cambridge
Known for	Enriched category theory
Awards	Centenary Medal
Scientific career
Fields	Mathematics
Institutions	University of Sydney
Thesis	Topics in Homology Theory  (1957)
Doctoral advisor	Shaun Wylie
Doctoral students	Ross 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 ${\cal {V}}$ be a monoidal category, and denote by ${\cal {V}}$-Cat the category of ${\cal {V}}$-enriched categories. Among other things, Kelly showed that ${\cal {V}}$-Cat has all weighted limits and colimits even when ${\cal {V}}$ 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.

External links

• 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
• 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