Proposition FF_disp_functor_ff_inv {C₁ C₂ : category} {F : C₁ ⟶ C₂} {D₁ : disp_cat C₁} {D₂ : disp_cat C₂} {FF : disp_functor F D₁ D₂} (HFF : disp_functor_ff FF) {x y : C₁} {f : x --> y} {xx : D₁ x} {yy : D₁ y} (ff : FF x xx -->[ (#F f) ] FF y yy) : ♯FF (disp_functor_ff_inv FF HFF ff) = ff. Proof. apply (homotweqinvweq ((disp_functor_ff_weq FF HFF xx yy f))). Qed.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.DisplayedCats.Core. Require Import UniMath.CategoryTheory.DisplayedCats.Isos.