nLab Saunders Mac Lane

Saunders MacLane (1909-2005) was one of the founders of category theory, with Samuel Eilenberg. Their 1945 paper General Theory of Natural Equivalences introduced category theory with the notions of categories, functors and natural transformations, motivated by formalizing the concept of dual objects.

Further with Eilenberg he developed of the strong links with group theory and group cohomology.

With Henry Whitehead he gave the first algebraic description of the homotopy 2-type of a space.

• Wikipedia entry

• MathGenealogy page

• MacTutor biography

• Colin McLarty: The Last Mathematician from Hilbert’s Göttingen: Saunders Mac Lane as Philosopher of Mathematics, Brit. J. Phil. Sci. 58 1 (2007) 77–112 [doi:10.1093/bjps/axl030]

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]

On abelian groups and identifying the category theoretic universal property of (co)products for the case of direct product groups (free product groups):

• Saunders MacLane: Groups, Categories and Duality, Proceedings of the National Academy of Sciences 34 6 (1948) [doi:10.1073/pnas.34.6.263]

• Saunders MacLane: Duality for Groups, Bulletin of the American Mathematical Society 56 6 (1950) 485–516 [doi:10.1090/S0002-9904-1950-09427-0]

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 and category theory:

• Saunders MacLane: Concepts and Categories in Perspective, in: A Century of Mathematics in America, Part I , Am. Math. Soc. (1988) 323–366. [ISBN 0-8218-0124-4, pdf]

On sheaf and topos theory:

• Saunders Mac Lane, Ieke Moerdijk: Sheaves in Geometry and Logic – A first introduction to topos theory, Springer (1992) & lbrack;doi:10.1007/978-1-4612-0927-0]

See also:

• Selected Papers. Edited by I. Kaplansky. Springer 1979

category: people