Lemma isaprop_is_inverse_in_precat {C : category} (a b : ob C) (f : a --> b) (g : b --> a) : isaprop (is_inverse_in_precat f g). Proof. apply isapropdirprod; apply homset_property. Qed.
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories.