Category

A collection of objects together with, for each ordered pair of objects X,Y, a set Hom(X,Y) of morphisms and an associative composition law ◦ : Hom(Y,Z)×Hom(X,Y) → Hom(X,Z) plus identity morphisms id_X for each object satisfying id_Y ◦ f = f and f ◦ id_X = f.