not to be confused with Daniel Kahn
Daniel Marinus Kan was a homotopy theorist working at MIT. He originated much of modern homotopy theory and category theory.
He got his PhD degree in 1955 from the Hebrew University of Jerusalem, advised by Samuel Eilenberg.
His PhD students include David L. Rector, Aldridge K. Bousfield, Stewart B. Priddy, Emmanuel Dror Farjoun, William G. Dwyer, Philip S. Hirschhorn, Jeffrey H. Smith, David A. Blanc.
Clark Barwick, Michael Hopkins, Haynes Miller, and Ieke Moerdijk, Daniel M. Kan (1927—2013), Notices of the American Mathematical Society, 62-09 (2015) (pdf, doi:10.1090/noti1282).
Clark Barwick has posted (on 7 August 2013) the following:
On Sunday, 4 August, 2013, Daniel M. Kan died peacefully at his home in Newton, MA, surrounded by his family. It was his 86th birthday. There was a small burial service Monday afternoon.
Dan received his Ph.D in 1955, and after short-term positions at Columbia, Princeton, and Hebrew University, he joined the Department of Mathematics at MIT in 1959, where he remained until his retirement in 1993. Dan continued to do mathematics until the last week of his life.
In his long career, Dan published more than 70 papers with 15 coauthors. His lifelong mathematical pursuit was abstract homotopy theory, and many of his ideas were so natural and flexible that they quickly became incorporated into the very fabric of algebraic topology. He supervised 15 Ph.D students (all of them at MIT), and he influenced many more through his unique seminar in algebraic topology, which today is known as the Kan Seminar.
On simplicial groups and introducing the simplicial loop group-functor:
Daniel M. Kan, A combinatorial definition of homotopy groups, Annals of Mathematics 67 2 (1958) 282–312 [doi:10.2307/1970006]
Daniel M. Kan, On homotopy theory and c.s.s. groups, Ann. of Math. 68 (1958) 38-53 [jstor:1970042]
On homotopy limits, completions and localizations (such as p-completion and rationalization):
Aldridge Bousfield, Daniel Kan, Localization and completion in homotopy theory, Bull. Amer. Math. Soc. 77 6 (1971) 1006-1010 [doi:10.1090/S0002-9904-1971-12837-9, pdf]
Daniel M. Kan and Aldridge K. Bousfield, Homotopy Limits, Completions and Localizations, Lecture Notes in Mathematics 304 (1972; 1987), Springer (doi:10.1007/978-3-540-38117-4)
On the core of a ring:
On derived hom-spaces (function complexes) in projective model structures on simplicial presheaves:
On the $G$-Borel model structure and its Quillen equivalence with the slice model structure over the simplicial classifying space $\overline W G$:
William Dwyer, Daniel Kan, Simplicial localizations of categories, J. Pure Appl. Algebra 17 3 (1980), 267-284 [doi:10.1016/0022-4049(80)90049-3, pdf]
William Dwyer, Daniel Kan, Calculating simplicial localizations, J. Pure Appl. Algebra 18 (1980), 17-35 [doi:10.1016/0022-4049(80)90113-9, pdf]
William Dwyer, Daniel Kan, Function complexes in homotopical algebra, Topology 19 (1980), 427-440 [doi:10.1016/0040-9383(80)90025-7, pdf]
William Dwyer, Daniel Kan, Equivalences between homotopy theories of diagrams, in: Algebraic topology and algebraic K-theory, Ann. of Math. Stud. 113, Princeton University Press (1988) [doi:10.1515/9781400882113-009]
On (enhancement and generalization of) Elmendorf's theorem in equivariant homotopy theory:
Introducing the model structure on simplicial groupoids:
On homotopy commutative diagrams:
On homotopy limits:
On derived functors such as homotopy limit-functors on model categories and more general homotopical categories:
Last revised on May 31, 2023 at 16:09:49. See the history of this page for a list of all contributions to it.