Definition functor_strongmon_equiv_layer {C D : bicat_of_univ_cats} (F : bicat_of_univ_cats⟦C,D⟧) (tuuaC : disp_univstrongfunctor C) (tuuaD : disp_univstrongfunctor D) : functor_strong_monoidal F (cmon_structure_from_layer (pr1 tuuaC)) (cmon_structure_from_layer (pr1 tuuaD)) ≃ tuuaC -->[F] tuuaD. Proof. use weqtotal2. { apply functor_laxmon_equiv_layer. } intro flm. use weqimplimpl. - intro flms. split ; apply flms. - intro flms. split ; apply flms. - apply isaprop_functor_strong. - simpl. apply isaprop_P_strong_preserving. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.NaturalTransformations. Require Import UniMath.Bicategories.Core.Bicat. Require Import UniMath.Bicategories.Core.Examples.BicatOfUnivCats. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.Bicategories.DisplayedBicats.DispBicat. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Sigma. Require Import UniMath.Bicategories.DisplayedBicats.Examples.Prod. Require Import UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.CurriedMonoidalCategories. Require Import UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.AssociatorUnitorsLayer. Require Import UniMath.Bicategories.MonoidalCategories.UnivalenceMonCat.FinalLayer. Import Notations.