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.

English Wikipedia entry
MacTutor biography
Colin McLarty, The Last Mathematician from Hilbert’s Göttingen: Saunders Mac Lane as Philosopher of Mathematics,Brit. J. Phil. Sci. 2007 (pdf)

Selected writings

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

Samuel Eilenberg, Saunders MacLane, Group Extensions and Homology, Annals of Mathematics 43 4 (1942) 757-831 [doi:10.2307/1968966, jstor:1968966]

Introducing category theory:

Samuel Eilenberg, Saunders MacLane, General Theory of Natural Equivalences, Transactions of the American Mathematical Society 58 2 (1945) 231-294 [doi:10.1090/S0002-9947-1945-0013131-6, jstor:1990284]

Introducing abstract group cohomology:

Samuel Eilenberg, Saunders MacLane, Cohomology Theory in Abstract Groups. I, Annals of Mathematics, Second Series 48 1 (1947) 51-78 [doi:10.2307/1969215]

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 $\overline{W}G$ :

Saunders MacLane, Constructions simpliciales acycliques, Colloque Henri Poincaré 1954 (pdf)

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:

S. Eilenberg, D. K. Harrison, S. MacLane, H. Röhrl (eds.): Proceedings of the Conference on Categorical Algebra - La Jolla 1965, Springer (1966) [doi:10.1007/978-3-642-99902-4]

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:

Saunders Mac Lane, Metric postulates for plane geometry, American Mathematical Monthly, 66 7 (1959) 543-555. (doi:10.2307/2309851, web)

On category theory:

Saunders MacLane, Categories for the Working Mathematician, Graduate Texts in Mathematics 5, Springer (1971, second ed. 1997) [doi:10.1007/978-1-4757-4721-8]

On homological algebra:

Saunders MacLane, Homology, Grundlehren der Mathematischen Wissenschaften 114, Springer (1963, 1974), reprinted as: Classics in Mathematics, Springer (1995) [pdf, doi:10.1007/978-3-642-62029-4]

On philosophy of mathematics:

Mathematics form and function, Springer 1986

On some history of mathematics:

Saunders Mac Lane: Concepts and Categories in Perspective, in: P. Duren, A century of mathematics in America Part 1, AMS (1988) 323-365. [pdf, ISBN:0-8218-0124-4]

On sheaf and topos theory:

Saunders MacLane, Ieke Moerdijk, Sheaves in Geometry and Logic, Springer (1992) [doi:10.1007/978-1-4612-0927-0]

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