Lemma actegory_prod_action_data_is_bifunctor : is_bifunctor actegory_prod_action_data. Proof. red; repeat split. * intros v cs. apply funextsec; intro i; apply (bifunctor_leftid (ActC i)). * intros cs v. apply funextsec; intro i; apply (bifunctor_rightid (ActC i)). * intros v cs1 cs2 cs3 fs1 fs2. apply funextsec; intro i; apply (bifunctor_leftcomp (ActC i)). * intros cs v1 v2 v3 h1 h2. apply funextsec; intro i; apply (bifunctor_rightcomp (ActC i)). * intros v1 v2 cs1 cs2 h fs. apply funextsec; intro i; apply (bifunctor_equalwhiskers (ActC i)). Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors. Require Import UniMath.CategoryTheory.Monoidal.Categories. Require Import UniMath.CategoryTheory.Monoidal.Functors. Require Import UniMath.CategoryTheory.Actegories.Actegories. Require Import UniMath.CategoryTheory.Actegories.MorphismsOfActegories. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.ProductCategory. Import BifunctorNotations. Import MonoidalNotations. Import ActegoryNotations.