Proposition isaset_twosided_disp_functor {C₁ C₁' C₂ C₂' : category} (F : C₁ ⟶ C₁') (G : C₂ ⟶ C₂') (D : strict_twosided_disp_cat C₁ C₂) (D' : strict_twosided_disp_cat C₁' C₂') : isaset (twosided_disp_functor F G D D'). Proof. use isaset_total2. - use isaset_total2. + repeat (use impred_isaset ; intro). apply is_strict_strict_twosided_disp_cat. + intro f ; cbn. repeat (use impred_isaset ; intro). apply isaset_disp_mor. - intro FG. use isasetaprop. apply isaprop_twosided_disp_functor_laws. Qed.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Prelude. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.DisplayedFunctor. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Isos. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Total.