The identity natural transformation of a functorπΉ:π’βπ£ is the natural transformation idπΉβπ£π’(πΉ,πΉ) whose component for every object π₯βπ’ is the identity morphism cat
(idπΉ)π₯=idπΉπ₯=πΉ(idπ₯)
The form the identity morphisms in the functor categoryπ£π’.