Lemma disp_functor_eq {C C':category} {F: functor C C'} {D:disp_cat C} {D':disp_cat C'} (DF DF': disp_functor F D D') : pr1 DF = pr1 DF' -> DF = DF'. Proof. intro H. apply (total2_paths_f H). apply proofirrelevance. apply isaprop_disp_functor_axioms. Defined.
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.