nLab
identity-assigning morphism

Definition

Given an internal category CC with object of objects C 0C_0 and object of morphisms C 1C_1, the identity-assigning morphism of CC is the morphism i:C 0C 1i: C_0 \to C_1 that is part of the definition of internal category.

This generalises the identity-assigning function of a small category CC. Given such a small category 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 simplicial sets and simplicial objects, the identity-assigning morphisms are the degeneracy maps .

Revised on March 30, 2010 19:15:32 by Urs Schreiber (87.212.203.135)