proposition: Lemma isfunctor_comm_functor_data {I A B : category} : ∏ (D:[I,[A,B]]) (a:A), is_functor (comm_functor_data D a).
proof: Proof. split. { unfold functor_idax. intro i; simpl. unfold functor_mor_application. now rewrite functor_id. } { intros i j k f g; simpl. unfold functor_mor_application. now rewrite functor_comp. } Qed.
imports: UniMath.Foundations.Preamble UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.RepresentableFunctors.Precategories UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.yoneda UniMath.CategoryTheory.Categories.HSET.Core