# Category theory

Category theory formalizes mathematical structure and its concepts in terms of a labeled directed graph called a category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms). A category has two basic properties: the ability to compose the arrows associatively, and the existence of an identity arrow for each object. The language of category theory has been used to formalize concepts of other high-level abstractions such as sets, rings, and groups. Informally, category theory is a general theory of functions. Several terms used in category theory, including the term "morphism", are used differently from their uses in the rest of mathematics. In category theory, morphisms obey conditions specific to category theory itself.

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treated in Categories, What’s the Point?

Perhaps primarily due to the prominence of monads in the Haskell programming language, programmers ar...

treated in What is Applied Category Theory?

This is a collection of introductory, expository notes on applied category theory, inspired by the 20...

treated in Categorical informatics

Category theory is a universal modeling language.