Section generalized.
Variables F G : Functor C D.
Hypothesis HO : object_of F = object_of G.
Hypothesis HM : transport (fun GO => forall s d,
morphism C s d
-> morphism D (GO s) (GO d))
HO
(morphism_of F)
= morphism_of G.
Local Notation CO c := (transport (fun GO => morphism D (F c) (GO c))
HO
(identity (F c))).
Definition generalized_identity_commutes s d (m : morphism C s d)
: CO d o morphism_of F m = morphism_of G m o CO s.

Lemma right_identity (F F' : Functor C D)
(T : NaturalTransformation F F')
: T o 1 = T.