Definition catiso_is_path_cat (C D : category) : C = D ≃ catiso C D. Proof. refine (catiso_is_path_precat _ _ (homset_property D) ∘ _)%weq. refine (path_sigma_hprop _ _ _ _). apply isaprop_has_homsets. 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.