Definition opposite_enriched_precat (A : enriched_precat Mon_V) : enriched_precat (_ ,, monoidal_swapped Mon_V). Proof. use make_enriched_precat. - use make_enriched_precat_data. + exact A. + intros x y. exact (enriched_cat_mor y x). + intro x. simpl. exact (enriched_cat_identity x). + intros x y z. exact (enriched_cat_comp z y x). - split; simpl in a, b; simpl. + refine (_ @ enriched_id_right b a). apply maponpaths_2. unfold monoidal_cat_tensor_mor. unfold functoronmorphisms1. cbn. rewrite whiskerscommutes ; [ apply idpath | ]. apply (pr2 Mon_V). + refine (_ @ enriched_id_left b a). apply maponpaths_2. unfold monoidal_cat_tensor_mor. unfold functoronmorphisms1. cbn. rewrite whiskerscommutes ; [ apply idpath | ]. apply (pr2 Mon_V). - intros a b c d ; cbn. refine (!(id_left _) @ _). etrans. { apply maponpaths_2. exact (!(mon_rassociator_lassociator _ _ _)). } rewrite !assoc'. apply maponpaths. refine (_ @ !(enriched_assoc d c b a) @ _). + apply maponpaths. apply maponpaths_2. unfold monoidal_cat_tensor_mor. unfold functoronmorphisms1. cbn. rewrite whiskerscommutes ; [ apply idpath | ]. apply (pr2 Mon_V). + apply maponpaths_2. 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.