Lemma type_precat_equiv_iso (A B : ob type_precat) : A ≃ B -> iso A B. Proof. intro f. use make_iso. - exact (pr1 f). - apply type_equiv_is_iso. Defined.
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.