identity natural transformation

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 the identities for vertical composition of natural transformations in the functor category D CD^C and in the 2-category Cat.

Last revised on December 14, 2009 at 04:08:10. See the history of this page for a list of all contributions to it.