Diagram (category theory)

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This article provides insufficient context for those unfamiliar with the subject. Please help improve the article by providing more context for the reader, especially: For most readers, diagrams are graphical representations such as those presented in commutative diagram; the article must starts with this, and explain why the content of the article is a formalization of this representation. (June 2023) (Learn how and when to remove this message)

In category theory, a branch of mathematics, a diagram is the categorical analogue of an indexed family in set theory. The primary difference is that in the categorical setting one has morphisms that also need indexing. An indexed family of sets is a collection of sets, indexed by a fixed set; equivalently, a function from a fixed index set to the class of sets. A diagram is a collection of objects and morphisms, indexed by a fixed category; equivalently, a functor from a fixed index category to some category.