Lemma reindexed_action_data_is_bifunctor: is_bifunctor reindexed_action_data. Proof. split5; red; intros; cbn. - apply (bifunctor_leftid Act). - rewrite functor_id. apply (bifunctor_rightid Act). - apply (bifunctor_leftcomp Act). - rewrite functor_comp. apply (bifunctor_rightcomp Act). - apply (bifunctor_equalwhiskers Act). 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.Monoidal.Examples.MonoidalPointedObjects. Require Import UniMath.CategoryTheory.Actegories.Actegories. Import BifunctorNotations. Import MonoidalNotations. Import ActegoryNotations.