proposition: 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: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Functors UniMath.CategoryTheory.Monoidal.Displayed.TotalMonoidal UniMath.CategoryTheory.Actegories.Actegories UniMath.CategoryTheory.Actegories.ConstructionOfActegories UniMath.CategoryTheory.coslicecat UniMath.CategoryTheory.Monoidal.Examples.MonoidalPointedObjects