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 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 the -Borel model structure and its Quillen equivalence with the slice model structure over the simplicial classifying space :
On (enhancement and generalization of) Elmendorf's theorem in equivariant homotopy theory:
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 July 16, 2022 at 12:57:00. See the history of this page for a list of all contributions to it.