Daniel Kan

Daniel Kan was born into a Jewish family. During World War II, Kan and his family were interned at the Bergen-Belsen concentration camp. Although the family survived the internment, his parents died of dysentery shortly after the camp's liberation, leaving Kan orphaned. 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, Emmanuel Dror Farjoun, and Jeffrey H. Smith. He was an emeritus professor at the Massachusetts Institute of Technology where he taught from 1959, formally retiring in 1993. ==Work==

He played a role in the beginnings of modern homotopy theory similar 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, the usual closed model category structure on the category of simplicial sets is known as Kan–Quillen model structure, while its fibrations and fibrant objects are known as Kan fibrations and Kan complexes respectively. Some of Kan's later work concerned model categories and other homotopical categories. Especially noteworthy are his work with Aldridge Bousfield on completions and homotopy limits, and his work with William Dwyer on simplicial localizations of relative categories. ==See also==