fact: Definition disp_cat_eq_functor : UU := ∑ (pob : ∏ (x : C), D₁ x ≃ D₂ x), ∑ (pmor : ∏ (x y : C) (xx : D₁ x) (yy : D₁ y) (f : x --> y), xx -->[ f ] yy ≃ pob x xx -->[ f ] pob y yy), (∏ (x : C) (xx : D₁ x), pmor _ _ _ _ _ (id_disp xx) = id_disp (pob x xx)) × (∏ (x y z : C) (f : x --> y) (g : y --> z) (xx : D₁ x) (yy : D₁ y) (zz : D₁ z) (ff : xx -->[ f ] yy) (gg : yy -->[ g ] zz), pmor _ _ _ _ _ (ff ;; gg) = pmor _ _ _ _ _ ff ;; pmor _ _ _ _ _ gg).
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Prelude UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Equivalences.Core UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Functors UniMath.CategoryTheory.DisplayedCats.NaturalTransformations UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.DisplayedCats.Equivalences UniMath.CategoryTheory.DisplayedCats.DisplayedFunctorEq UniMath.CategoryTheory.DisplayedCats.EquivalenceOverId