nLab Saunders Mac Lane

Selected writings

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.

Selected writings

On group extensions and group homology via Ext/Tor-functors:

Introducing category theory:

Introducing abstract group cohomology:

Introducing Eilenberg-MacLane spaces:

Introducing the simplicial classifying space construction W¯G\overline{W}G:

On homotopy 2-types (N.B. their 3-type is the modern 2-type)

  • (with J. H. C. Whitehead) On the 3-type of a complex, Proc. Nat. Acad. Sci. U.S.A., 36 (1950) 41-48

On categorical algebra:

On classical mechanics:

  • Geometrical Mechanics, Lectures 1968 (web

On Grothendieck universes in the mathematical foundations of category theory:

  • Saunders MacLane, One universe as a foundation for category theory, In: Reports of the Midwest Category Seminar III, Lecture Notes in Mathematics 106, Springer (1969) 192-200 [doi:10.1007/BFb0059147]

On geometric realization of simplicial topological spaces for constructing classifying spaces, understood as simplicial coends in compactly generated topological spaces:

  • Saunders MacLane, The Milgram bar construction as a tensor product of functors, In: F.P. Peterson (eds.) The Steenrod Algebra and Its Applications: A Conference to Celebrate N.E. Steenrod’s Sixtieth Birthday, Lecture Notes in Mathematics 168, Springer 1970 (doi:10.1007/BFb0058523, pdf)

On Euclidean geometry:

On category theory:

On homological algebra:

On philosophy of mathematics:

  • Mathematics form and function, Springer 1986

On some history of mathematics:

On sheaf and topos theory:


See also:

  • Selected Papers. Edited by I. Kaplansky. Springer 1979
category: people

Last revised on November 16, 2023 at 07:36:50. See the history of this page for a list of all contributions to it.