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The History of Category Theory

Category Theory was founded by an article which Samuel Eilenberg and Saunders Mac Lane published in 1945 in the Transactions of the American Mathematical Society Vol. 58, pp. 231-294. The title of the article was "General theory of natural equivalences." During the 1950's Alexander Grothendieck and others utilized Category Theory quite xiccessfully in the field of algebraic geometry. In the 1960's Francis William Lawvere applied it to logic. Subsequently it has been applied fruitfully in computer science, linguistics and philosophy, among other fields.

A crucial development was the concept of functors, a mapping between categories. This made categories and functors as the objects and arrows of a category.

The next step was the definition of a natural transformation and the concept of adjunction; i.e., adjoint functors.

(To be continued.)

For more topics in Category Theory see Topics in Category Theory.

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