Outline of category theory

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The following outline is provided as an overview of and guide to category theory:

Contents

Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the mid-20th century in their foundational work on algebraic topology. Category theory is used in most areas of mathematics. In particular, many constructions of new mathematical objects from previous ones that appear similarly in several contexts are conveniently expressed and unified in terms of categories. Examples include quotient spaces, direct products, completion, and duality.

Many areas of computer science also rely on category theory, such as functional programming and semantics.

Essence of category theory

Branches of category theory

Specific categories

Objects

Morphisms

Functors

Limits

Additive structure

Dagger categories

Monoidal categories

Structure

Topoi, toposes

History of category theory

Persons influential in the field of category theory

Category theory scholars

See also