Definition cat_equiv_to_catiso_weq (C D : precategory) : cat_equiv C D ≃ catiso C D. Proof. refine (cat_equiv_to_catiso C D ,, _). use isweq_iso. - exact (catiso_to_cat_equiv C D). - reflexivity. - reflexivity. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.whiskering. Require Import UniMath.CategoryTheory.catiso.