identity-assigning morphism

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

This generalises the **identity-assigning function** of a small category $C$. Given such a small category with set of objects $C_0$ and set of morphisms $C_1$, the **identity-assigning function** of $C$ is the function $i: C_0 \to C_1$ that maps each object in $C_0$ to its identity morphism in $C_1$.

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)