Daniel Kan

 ( 1927 Births ) 

Daniel Marinus Kan (or simply Dan Kan) (August 4, 1927 – August 4, 2013) was a Dutch mathematician working in category theory and homotopy theory. He was a prolific contributor to both fields for six decades, having authored or coauthored several dozen research papers and monographs.

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Career Daniel Kan was born into a Jewish family. 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.

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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 category theory 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 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 and respectively.

Some of Kan's later work concerned model category and other homotopical categories. Especially noteworthy are his work with Aldridge Bousfield on completions and homotopy colimit, and his work with William Dwyer on simplicial localizations of relative categories.

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See also

• Dold–Kan correspondence
• Kan extension

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External links

• Kan memorial note at the MIT Mathematics Department

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