nLab
identity morphism

Context

Equality and Equivalence

Category theory

Contents

Idea

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.

Is there a wide-spread notation for identity morphism on a specified object of a specific category CC? (I consider several categories and there are several different identity morphisms (one for each category) on the same object.)

Revised on May 20, 2015 17:12:39 by Victor Porton (84.228.118.24)