fact: Definition precategory_total_comp (C : precategory_data) : ∏ f g : total_morphisms C, precategory_target C f = precategory_source C g -> total_morphisms C := λ f g e, tpair _ (make_dirprod (pr1 (pr1 f))(pr2 (pr1 g))) ((pr2 f · idtomor _ _ e) · pr2 g).
imports: UniMath.Foundations.PartA UniMath.Foundations.Sets UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Setcategories