Proposition catiso_reflect_ob_eq {x y : C} (p : F x = F y) : x = y. Proof. refine (!(catiso_inv_ob_catiso x) @ _ @ catiso_inv_ob_catiso y). apply maponpaths. exact p. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.Foundations.UnivalenceAxiom. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Setcategories. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.Adjunctions.Core. Require Import UniMath.CategoryTheory.Equivalences.Core. Require Import UniMath.CategoryTheory.Equivalences.FullyFaithful.