Daniel Kan at his home.
August 4, 1927|
|Died||August 4, 2013|
|Alma mater||Hebrew University of Jerusalem|
|Institutions||Massachusetts Institute of Technology|
|Doctoral advisor||Samuel Eilenberg|
William Gerard Dwyer|
Jeffrey H. Smith
Daniel Marinus Kan (or simply Dan Kan) (August 4, 1927 – August 4, 2013) was a Jewish mathematician working in homotopy theory. He was a prolific contributor to the field for the last six decades, having authored or coauthored several dozen research papers and monographs. The general theme of his career had been abstract homotopy theory.
He was an emeritus professor at the Massachusetts Institute of Technology, where he taught since the early 1960s. He received his Ph.D. at Hebrew University in 1955, under the direction of Samuel Eilenberg. His students include Aldridge K. Bousfield, William Dwyer, Stewart Priddy, and Jeffrey H. Smith.
He played a role in the beginnings of modern homotopy theory perhaps analogous to that of Saunders Mac Lane in homological algebra, namely the adroit and persistent application of categorical methods. His most famous work is the abstract formulation of the discovery of adjoint functors, which dates from 1958. The Kan extension is one of the broadest descriptions of a useful general class of adjunctions.
From the mid-1950s he made distinguished contributions to the theory of simplicial sets and simplicial methods in topology in general. In recognition of this, fibrations in the usual closed model category structure on the category of simplicial sets are known as Kan fibrations, and the fibrant objects are known as Kan complexes.
Some of Kan's more recent work concerned model categories and other homotopical categories. Especially noteworthy are his work with Bousfield on completions and homotopy limits, and his work with Dwyer on simplicial localizations of relative categories.