Definition catiso_is_path_precat (C D : precategory) (HD : has_homsets D) : C = D ≃ catiso C D := ((cat_equiv_to_catiso_weq C D) ∘ weq_cat_eq_cat_equiv C D ∘ cat_eq_1_to_cat_eq_2 C D HD ∘ cat_path_to_cat_eq_1 C D ∘ path_precat C D HD)%weq.
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.