proposition: Lemma weq_hom' {c1 : C} {c2 : C} (f : C ⟦ c1, c2 ⟧) : ∃! x : (∑ f0 : C ⟦ c1, c2 ⟧, pr1 (uo c1) -->[ f0] pr1 (uo c2)), pr1 x = f.
proof: Proof. use tpair. - simple refine ((_ ,, _) ,, _). + exact f. + apply (pr1 (is_contr_disp_mor _ _ f)). + apply idpath. - intros [[g gg] p]. use subtypePath. { intro ; apply homset_property. } use subtypePath. { intro. apply isapropifcontr. apply is_contr_disp_mor. } exact p. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.catiso UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Isos UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.Univalence