Daniel Kan

Who is Daniel Kan?

Daniel Marinus Kan was a Dutch 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 has been abstract homotopy theory.

He was an emeritus professor at MIT, where he has 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.

He has also made contributions to the theory of simplicial sets and simplicial methods in topology in general: 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.