chapter  1
10 Pages

A Taste of Category Theory

Acategory C consists of a class of objects together with sets HomC(X, Y ), for any pair of objects X, Y of C, satisfying suitable conditions listed hereafter. The elements of HomC are called C-morphisms or just morphisms, if there is no ambiguity concerning the category considered. For any object X of C there is a distinguished element IX ∈ HomC(X, X ), called the identity morphism of X . For any triple X, Y, Z of objects in C there is a composition map:

HomC(X, Y )×HomC(Y, Z ) → HomC(X, Z ), ( f, g) → g ◦ f such that the following properties hold:

i. For f ∈HomC(X, Y ), g ∈ HomC(Y, Z ), h ∈ HomC(Z , W ) we have: h◦(g◦ f ) = (h ◦ g) ◦ f .