Lemma pointedtensorialstrength_preserves_unitor {C : category} (M : monoidal C) {F : functor C C} (pts : pointedtensorialstrength M F): preserves_unitor _ _ _ _ pts ≃ ∏ c : C, pts I_{ monoidal_pointed_objects M} c · # F lu^{M}_{c} = lu^{M}_{F c}. Proof. use weqimplimpl. - intros H c. assert (Hc := H c). clear H. cbn in Hc. unfold total_unit, reindexed_action_unitor_data in Hc. cbn in Hc. do 2 rewrite (bifunctor_rightid M) in Hc. do 2 rewrite id_left in Hc. exact Hc. - intros H c. cbn. unfold total_unit, reindexed_action_unitor_data. cbn. do 2 rewrite (bifunctor_rightid M). do 2 rewrite id_left. apply H. - apply impred; intro c. apply C. - apply impred; intro c. apply C. 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.Displayed.TotalMonoidal. Require Import UniMath.CategoryTheory.Actegories.Actegories. Require Import UniMath.CategoryTheory.Actegories.ConstructionOfActegories. Require Import UniMath.CategoryTheory.coslicecat. Require Import UniMath.CategoryTheory.Monoidal.Examples.MonoidalPointedObjects. Import BifunctorNotations. Import MonoidalNotations. Import ActegoryNotations.