## Quick Reference

A collection of *objects A*, together with a related set of **morphisms***M*. An object is a generalization of a set and a morphism is a generalization of a function that maps between sets.

The set *M* is the disjoint union of sets of the form [*A*,*B*], where *A* and *B* are elements of *A*; if α is a member of [*A*,*B*], *A* is the **domain** of α, *B* is the **codomain** of α, and α is said to be a morphism from *A* to *B*. For each triple (*A*,*B*,*C*) of elements of *A* there is a dyadic operation ° from the Cartesian product[*B*,*C*] × [*A*,*B*]to [*A*,*C*]. The image β°α of the ordered pair (β,α) is the **composition** of β with α; the composition operation is associative. In addition, when the composition is defined there is an **identity** morphism for each *A* in *A*.

[*B*,*C*] × [*A*,*B*]

Examples of categories include the set of groups and homomorphisms on groups, and the set of rings and homomorphisms on rings. See functor.

**From:**
category
in
A Dictionary of Computing »

*Subjects:*
Computing.