Definition precomp_monoidal_catiso : catiso (total_category (functor_monoidal_disp_cat (TransportedLeftUnitor Duniv H_eso H_ff TC I lu) luE (TransportedRightUnitor Duniv H_eso H_ff TC I ru) ruE (TransportedAssociator Duniv H_eso H_ff TC α) αE )) (total_category (functor_monoidal_disp_cat lu luE ru ruE α αE )). Proof. use (adj_equivalence_of_cats_to_cat_iso precomp_monoidal_adj_equiv _ _). - apply is_univalent_LaxMonoidalFunctorCategory. - apply is_univalent_LaxMonoidalFunctorCategory'. 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.Core.Univalence. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.catiso. Require Import UniMath.CategoryTheory.FunctorCategory. Require Import UniMath.CategoryTheory.PrecompEquivalence. Require Import UniMath.CategoryTheory.ProductCategory. Require Import UniMath.CategoryTheory.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.DisplayedCats.Total. Require Import UniMath.CategoryTheory.DisplayedCats.TotalCategoryFacts. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions.Product. Require Import UniMath.CategoryTheory.DisplayedCats.Constructions.FullSubcategory. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalCategoriesTensored. Require Import UniMath.CategoryTheory.Monoidal.AlternativeDefinitions.MonoidalFunctorCategory. Require Import UniMath.CategoryTheory.Monoidal.RezkCompletion.LiftedTensor. Require Import UniMath.CategoryTheory.Monoidal.RezkCompletion.LiftedTensorUnit. Require Import UniMath.CategoryTheory.Monoidal.RezkCompletion.LiftedUnitors. Require Import UniMath.CategoryTheory.Monoidal.RezkCompletion.LiftedAssociator.