nLab Daniel Kan

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 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.

Selected writings

On simplicial groups and introducing the simplicial loop group-functor:

On homotopy limits, completions and localizations (such as p-completion and rationalization):

On the core of a ring:

On derived hom-spaces (function complexes) in projective model structures on simplicial presheaves:

On the GG-Borel model structure and its Quillen equivalence with the slice model structure over the simplicial classifying space W¯G\overline W G:

On simplicial localization:

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:

category: people

Last revised on May 31, 2023 at 16:09:49. See the history of this page for a list of all contributions to it.