proposition: Lemma universalObjectFunctor_comm (C:category) {X Y:RepresentedFunctor C} (p:X-->Y) : p ⟳ universalElement (pr2 X) = universalElement (pr2 Y) ⟲ universalObjectFunctor C ▭ p.
proof: Proof. change (universalObjectFunctor C ▭ p) with (pr2 Y \\ (p ⟳ pr2 X)). apply pathsinv0, universalMapProperty. Defined.
imports: UniMath.Foundations.Preamble UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.Univalence UniMath.CategoryTheory.opp_precat UniMath.CategoryTheory.yoneda UniMath.CategoryTheory.Categories.HSET.Core UniMath.CategoryTheory.Categories.HSET.MonoEpiIso UniMath.CategoryTheory.RepresentableFunctors.Bifunctor UniMath.CategoryTheory.RepresentableFunctors.Precategories UniMath.MoreFoundations.Tactics