Daniel Kan

Daniel Marinus Kan (* August 4, 1927; † August 4, 2013 in Newton, Massachusetts, United States) was a mathematician who worked in the field of homotopy theory. Over the last five decades of his life, he composed in this field as an author or co-author of dozens of articles and monographs.

Career

Kan received his doctorate in 1955 under Samuel Eilenberg at the Hebrew University of Jerusalem. Since the early 1960s, he taught at MIT and is now professor emeritus.

Its importance for the beginnings of modern homotopy theory is perhaps comparable to that of Saunders Mac Lane for homological algebra, in that he consistently began Methods of category theory. His most famous work is the abstract formulation of the Adjungiertheit of functors from the year 1958.

Kan also contributed to the theory of simplicial sets, and generally simplicial methods in the topology. He gave a combinatorial definition of homotopy groups for Kan complexes ( semisimpliziale complexes that have the Kan extension property), for the singular chain complex of a topological space, the usual - provides homotopy groups of the space - topologically defined.

His doctoral include William G. Dwyer and Aldridge Bousfield ( a spectral sequence is named after Bousfield and Kan).

Writings

• On c. s s complexes. Amer. J. Math 79 (1957 ), 449-476.
• A combinatorial definition of homotopy groups. Ann. of Math (2) 67 1958 282-312.
• Adjoint functors. Trans Amer. Math Soc. 87 1958 294-329.
• With Bousfield: The homotopy spectral sequence of a space with coefficients in a ring. Topology 11 1972 79-106.
• With Bousfield: Homotopy limits, completions and Localizations. Lecture Notes in Mathematics, Vol 304 Springer -Verlag, Berlin-New York, 1972. V 348 pp.
• With Thurston: Every connected space Has the homology of a. Topology 15 (1976 ), no 3, 253-258.
• With Dwyer: Function complexes in homotopical algebra. Topology 19 (1980 ), no 4, 427-440.