Definition two_sided_disp_functor_weq_disp_functor {C₁ C₁' C₂ C₂' : category} (F : C₁ ⟶ C₁') (G : C₂ ⟶ C₂') (D₁ : twosided_disp_cat C₁ C₂) (D₂ : twosided_disp_cat C₁' C₂') : twosided_disp_functor F G D₁ D₂ ≃ disp_functor (pair_functor F G) (twosided_disp_cat_to_disp_cat _ _ D₁) (twosided_disp_cat_to_disp_cat _ _ D₂). Proof. use weq_iso. - exact two_sided_disp_functor_to_disp_functor. - exact disp_functor_to_two_sided_disp_functor. - abstract (intros FG ; use subtypePath ; [ intro ; apply isaprop_twosided_disp_functor_laws | ] ; apply idpath). - abstract (intros FG ; use subtypePath ; [ intro ; apply isaprop_disp_functor_axioms | ] ; apply idpath). 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.PrecategoryBinProduct. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Functors. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.TwoSidedDispCat. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Univalence. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Discrete. Require Import UniMath.CategoryTheory.TwoSidedDisplayedCats.Total. Section FromDispFunctor. End FromDispFunctor.