With "Sammy" Eilenberg, Saunders Mac Lane was one of the original pioneers of category theory. He initially worked on it as a language to enable ‘natural transformations’ to be described in a ‘natural’ way, and also developed, again with Eilenberg many of the strong links with group theory and the cohomology of groups. He was the author of one of the key books on homological algebra, see below.
With Henry Whitehead he gave the first algebraic description of the homotopy 2-type of a space.
Colin McLarty, The Last Mathematician from Hilbert’s Göttingen: Saunders Mac Lane as Philosopher of Mathematics,Brit. J. Phil. Sci. 2007 (pdf)
Introducing Eilenberg-MacLane spaces:
Samuel Eilenberg, Saunders Mac Lane, On the Groups $H(\Pi,n)$, I, Annals of Mathematics Second Series, Vol. 58, No. 1 (Jul., 1953), pp. 55-106 (jstor:1969820)
Samuel Eilenberg, Saunders Mac Lane, On the Groups $H(\Pi,n)$, II: Methods of Computation, Annals of Mathematics Second Series, Vol. 60, No. 1 (Jul., 1954), pp. 49-139 (jstor:1969702)
Samuel Eilenberg, Saunders Mac Lane, On the Groups $H(\Pi,n)$, III: Operations and Obstructions, Annals of Mathematics Second Series, Vol. 60, No. 3 (Nov., 1954), pp. 513-557 (jstor:1969849)
Introducing the simplicial classifying space construction $\overline{W}G$:
On Grothendieck universes in the mathematical foundations of category theory:
On geometric realization of simplicial topological spaces for constructing classifying spaces, understood as simplicial coends in compactly generated topological spaces:
On category theory:
On homotopy 3-types:
See also:
Last revised on January 22, 2023 at 11:54:20. See the history of this page for a list of all contributions to it.