Definition actegory_prod_action_data : bifunctor_data V PC PC. Proof. use make_bifunctor_data. * intros v cs. exact (fun (i: I) => v ⊗_{ActC i} (cs i)). * intros v cs1 cs2 fs. exact (fun (i: I) => v ⊗^{ActC i}_{l} (fs i)). * intros cs v1 v2 h. exact (fun (i: I) => h ⊗^{ActC i}_{r} (cs i)). Defined.
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.