nLab
identity natural transformation

Contents

Context

Equality and Equivalence

Category theory

Contents

Definition

The identity natural transformation on a functor F:CDF: C \to D is the natural transformation id F:FFid_F: F \to F that maps each object xx of CC to the identity morphism id F(x)id_{F(x)} in DD.

The identity natural transformations are themselves the identity morphisms for vertical composition of natural transformations in the functor category D CD^C and in the 2-category Cat.

Last revised on December 1, 2019 at 04:13:54. See the history of this page for a list of all contributions to it.