Definition precategory_total_id (C : precategory_data) : ob C -> total_morphisms C := λ c, tpair _ (make_dirprod c c) (identity c).
Require Import UniMath.Foundations.PartA. Require Import UniMath.Foundations.Sets. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Setcategories.