Category Theory: Early Stages

Abstract

The concepts of “Category” and “Functor” were first defined by Samuel Eilenberg and Saunders Mac Lane in 1942. This initial presentation did not elicit any special interest among contemporary mathematicians. Many years were still needed until the theory became an autonomous mathematical discipline. Since the 1960s category theory has afforded a unifying conceptual framework enabling a fairly effective manipulation of concepts belonging to branches like algebra, topology, logic and others, from a single, unified perspective. The generalizing possibilities afforded by category theory also led to several attempts at providing an abstract foundation for all of mathematics in terms of categorical concepts, in the hope of overcoming the difficulties encountered when this task was attempted from the set-theoretical point of view.