Definition is_disp_inverse {C : precategory} {D : disp_cat_data C} {x y : C} {f : x --> y} {g: y --> x} (isinv: is_inverse_in_precat f g) {xx : D x} {yy : D y} (ff : xx -->[f] yy) (gg : yy -->[g] xx) : UU := gg ;; ff = transportb _ (pr2 isinv) (id_disp yy) × ff ;; gg = transportb _ (pr1 isinv) (id_disp xx).
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.DisplayedCats.Core.