Lemma eq_in_sub_precategory (C : category)(C':sub_precategories C) (a b : sub_ob C') (f g : sub_precategory_morphisms C' a b) : pr1 f = pr1 g -> f = g. Proof. intro H. apply (total2_paths_f H). apply proofirrelevance. apply pr2. Qed.
Require Import UniMath.Foundations.Sets. Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Functors. Require Import UniMath.CategoryTheory.Core.Isos.