Lemma type_equiv_iso_is_equiv (A B : ob type_precat) : isweq (type_precat_equiv_iso A B). Proof. apply (isweq_iso _ (type_iso_equiv A B)). { intro f. apply subtypePath. { intro; apply isapropisweq. } reflexivity. } intro; apply eq_iso. reflexivity. Qed.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Monics. Require Import UniMath.CategoryTheory.Epis. Require Import UniMath.CategoryTheory.Categories.Type.Core.