# Allegory (mathematics)

## From Wikipedia, the free encyclopedia

In the mathematical field of category theory, an **allegory** is a category that has some of the structure of the category **Rel** of sets and binary relations between them. Allegories can be used as an abstraction of categories of relations, and in this sense the theory of allegories is a generalization of relation algebra to relations between different sorts. Allegories are also useful in defining and investigating certain constructions in category theory, such as exact completions.

In this article we adopt the convention that morphisms compose from right to left, so *RS* means "first do S, then do R".