identity morphism


Equality and Equivalence

Category theory



The identity morphism, or simply identity, of an object xx in some category CC is the morphism 1 x:xx1_x: x \to x, or id x:xx\id_x: x \to x, which acts as a two-sided identity for composition.

Given a small category CC with set of objects C 0C_0 and set of morphisms C 1C_1, the identity assigning function of CC is the function i:C 0C 1i: C_0 \to C_1 that maps each object in C 0C_0 to its identity morphism in C 1C_1.

For the generalisation to an internal category CC, see identity-assigning morphism.

In Set, the identity morphisms are the identity functions.

Revised on July 2, 2017 09:26:47 by Urs Schreiber (