Definition actegory_prod_data : actegory_data Mon_V PC. Proof. use make_actegory_data. - exact actegory_prod_action_data. - intros cs. intro i. apply au_{ActC i}. - intros cs. intro i. exact (auinv^{ActC i}_{_}). - intros v w cs. intro i. exact (aα^{ActC i}_{_,_,_}). - intros v w cs. intro i. exact (aαinv^{ActC 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.