General theory of natural equivalences

Abstract

Categories, functors, natural transformations, limits and colimits appeared almost out of nowhere in 1945 in Eilenberg & Mac Lane’s paper entitled "General Theory of Natural Equivalences". We said "almost", because when one looks at their 1942 paper "Group Extensions and Homology", one discovers specific functors and natural transformations at work. In fact, it was basically the need to clarify and abstract from their 1942 results that Eilenberg & Mac Lane came up with the notions of category theory.