Definition nattrans_laxmon_equiv_layer {C D : bicat_of_univ_cats} {F G : bicat_of_univ_cats⟦C,D⟧} (α : F ==> G) {tuuaC : disp_univmon C} {tuuaD : disp_univmon D} (ptuuaF : tuuaC -->[F] tuuaD) (ptuuaG : tuuaC -->[G] tuuaD) : nattrans_tensor_unit (functor_laxmon_from_layer _ _ _ ptuuaF) (functor_laxmon_from_layer _ _ _ ptuuaG) α ≃ ptuuaF ==>[α] ptuuaG. Proof. use weq_iso. - apply nattrans_laxmon_to_layer. - apply nattrans_laxmon_from_layer. - intro ; apply idpath. - intro. repeat (use total2_paths_f) ; try (apply idpath) ; try (apply isapropunit). 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.