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.
Introducing the Eilenberg-Steenrod axioms for ordinary cohomology:
Introducing simplicial sets and semi-simplicial sets (see the historical remarks here):
Introducing the Eilenberg-Zilber theorem:
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)
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