proposition: Lemma Signature_category_mor_diagram_pointwise (Hc : ∏ c, pr1 f1 c · pr1 f2 c = pr1 (α X) ((pr1 Y) c) · pr1 g2 c) : Signature_category_mor_diagram.
proof: Proof. apply nat_trans_eq_alt; intro c; simpl. unfold horcomp_data; simpl. rewrite functor_id, id_right; apply (Hc c). Qed.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.Tactics UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Coproducts UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.PointedFunctors UniMath.CategoryTheory.PointedFunctorsComposition UniMath.CategoryTheory.HorizontalComposition UniMath.CategoryTheory.FunctorCategory UniMath.SubstitutionSystems.Notation UniMath.SubstitutionSystems.Signatures UniMath.CategoryTheory.DisplayedCats.Core UniMath.CategoryTheory.DisplayedCats.Total UniMath.CategoryTheory.DisplayedCats.SIP UniMath.CategoryTheory.DisplayedCats.Univalence UniMath.CategoryTheory.Core.Univalence UniMath.SubstitutionSystems.BinProductOfSignatures UniMath.SubstitutionSystems.SumOfSignatures