Lemma isfunctor_comm_functor_data {I A B : category} : ∏ (D:[I,[A,B]]) (a:A), is_functor (comm_functor_data D a). 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.
Require Import UniMath.Foundations.Preamble. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.RepresentableFunctors.Precategories. Require Import UniMath.MoreFoundations.Tactics.