# nLab identity natural transformation

The identity natural transformation on a functor $F: C \to D$ is the natural transformation $id_F: F \to F$ that maps each object $x$ of $C$ to the identity morphism $id_{F(x)}$ in $D$. The identity natural transformations are the identities for vertical composition of natural transformations in the functor category $D^C$ and in the 2-category Cat.

Revised on December 14, 2009 04:08:10 by Toby Bartels (173.60.119.197)