# 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

Introducing Eilenberg-MacLane spaces:

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

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)
• Homology, number 114 in Grundlehren, Springer 1967 (pdf)
• Mathematics form and function, Springer 1986
• (with J. H. C. Whitehead) On the 3-type of a complex, Proc. Nat. Acad. Sci. U.S.A., 36, (1950), 41 – 48 (N.B. Their 3-type is the modern 2-type.)
• Geometrical Mechanics, Lectures 1968 (web)