fact: Definition total_morphisms (C : precategory_ob_mor) := total2 ( fun ab : dirprod (ob C)(ob C) => precategory_morphisms (pr1 ab) (pr2 ab)).
imports: UniMath.Foundations.PartA UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Setcategories