Definition opposite_enriched_nat_trans {A B : enriched_precat Mon_V} {F G : enriched_functor A B} (a : enriched_nat_trans F G) : enriched_nat_trans (opposite_enriched_functor G) (opposite_enriched_functor F). Proof. use make_enriched_nat_trans. - intro x. exact (a x). - intros x y. cbn. apply pathsinv0. refine (_ @ enriched_nat_trans_ax a y x @ _). + apply maponpaths. unfold precompose_underlying_morphism, postcompose_underlying_morphism. unfold monoidal_cat_tensor_mor. unfold functoronmorphisms1. cbn. rewrite <- whiskerscommutes ; [ apply idpath | ]. apply (pr2 Mon_V). + apply maponpaths. unfold precompose_underlying_morphism, postcompose_underlying_morphism. unfold monoidal_cat_tensor_mor. unfold functoronmorphisms1. cbn. rewrite <- whiskerscommutes ; [ apply idpath | ]. apply (pr2 Mon_V). 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.EnrichedCats.Enriched.Enriched. Import MonoidalNotations.