proposition: Lemma weq_hom {c1 : C} {c2 : C} (d1 : D c1) (d2 : D c2) (f : C ⟦ c1, c2 ⟧) : ∃! x : (∑ f0 : C ⟦ c1, c2 ⟧, d1 -->[ f0] d2), pr1 x = f.
proof: Proof. use tpair. - simple refine ((_ ,, _) ,, _). + exact f. + apply uf0. + apply idpath. - cbn. intros [[g gg] q]. use subtypePath. { intro ; apply homset_property. } use subtypePath. { intro. apply isapropifcontr. apply uf0. } exact q. 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