Definition path_precat (C D : precategory) (HD : has_homsets D) : C = D ≃ precategory_data_from_precategory C = D. Proof. refine (path_sigma_hprop _ _ _ _). apply isaprop_is_precategory. apply HD. 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.