nLab Samuel Eilenberg

Samuel ‘Sammy’ Eilenberg (1913-1998) was one of the founders of category theory, with Saunders Mac Lane. 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.

• Wikipedia entry

• MathGenealogy page

• Hyman Bass, Henri Cartan, Peter Freyd, Alex Heller, Saunders Mac Lane:
  

  Samuel Eilenberg (1913–1998),
  Notices of the AMS 45 9 (Oct 1998) 1344-1352 [pdf]

Selected students

• Alex Heller (1950)

• Kuo Tsai Chen (1950)

• David Buchsbaum (1954)

• Daniel Kan (1955)

• William Lawvere (1963)

• Harry Applegate (1965)

• Myles Tierney (1965)

• Jonathan Beck (1967)

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 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 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 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), Princeton Mathematical Series 19 (1999) [ISBN:9780691049915, doi:10.1515/9781400883844, 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