nLab Samuel Eilenberg

With Saunders Mac Lane, ‘Sammy’ Eilenberg was one of the ‘fathers’ of category theory. In their 1945 paper General Theory of Natural Equivalences they introduced the definition of category. The reason for introducing categories was to introduce functors, and the reason for introducing functors was to introduce natural transformations (more specifically natural equivalences) in order to define what natural means in mathematics.

• Wikipedia entry

Selected writings

Introducing the Eilenberg-Steenrod axioms for ordinary cohomology:

• Samuel Eilenberg, Norman E. Steenrod, Axiomatic Approach to Homology Theory, Proceedings of the National Academy of Sciences 31 4 (1945) 117–120 [doi:10.1073/pnas.31.4.117]

Introducing simplicial sets and semi-simplicial sets (see the historical remarks here):

• Samuel Eilenberg, Joseph Zilber, Semi-Simplicial Complexes and Singular Homology, Annals of Mathematics vol. 51 no. 3 (1950), 499–513 (jstor:1969364)

On algebraic topology:

• Samuel Eilenberg, Norman Steenrod, Foundations of Algebraic Topology, Princeton University Press 1952 (pdf, ISBN:9780691653297)

Introducing the Eilenberg-Zilber theorem:

• Samuel Eilenberg, Joseph Zilber, On Products of Complexes, Amer. Jour. Math. 75 (1): 200–204, (1953) (jstor:2372629)

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)

On separable algebras and Frobenius algebras:

• Samuel Eilenberg, Tadasi Nakayama, On the dimension of modules and algebras. II. Frobenius algebras and quasi-Frobenius rings, Nagoya Math. J. 9 (1955) 1-16 [euclid]

On homological algebra:

• Henri Cartan, Samuel Eilenberg, Homological algebra, Princeton Univ. Press (1956) (ISBN:9780691049915, pdf)

On homology of loop spaces:

• Samuel Eilenberg, John Moore, Homology and fibrations, Comment. Math. Helv., 40 (1966), pp. 199-236 (pdf)

Introducing the notion of closed categories:

• Samuel Eilenberg, G. Max Kelly, Closed Categories, pp. 421-562 in: 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 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]

Related entries

• category theory

• Eilenberg-MacLane space

• history of cohomology with local coefficients

category: people