nLab
identity anafunctor

The identity anafunctor on a category $C$ is the anafunctor ${\mathrm{id}}_C:C\to C$ that, as a span of functors, looks like $C\stackrel{{\mathrm{id}}_C}{\leftarrow }C\stackrel{{\mathrm{id}}_C}{\to }C$, where now ${\mathrm{id}}_C$ is the identity functor on $C$. Of course, this is the same as the identity functor on $C$ interpreted as an anafunctor.

The identity anafunctors are the identities for composition of anafunctors in Cat.