proposition: Lemma is_omega_cocont_BinProduct_of_Signatures (S1 S2 : Signature C D D') (h1 : is_omega_cocont S1) (h2 : is_omega_cocont S2) (PC: BinProducts D') (hE : ∏ x, is_omega_cocont (constprod_functor1 (BinProducts_functor_precat C D PD) x)) : is_omega_cocont (BinProduct_of_Signatures S1 S2).
proof: Proof. apply is_omega_cocont_BinProduct_of_functors; try assumption. apply (BinProducts_functor_precat _ _ PC). Defined.
imports: UniMath.Foundations.PartD UniMath.MoreFoundations.PartA UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.FunctorCategory UniMath.CategoryTheory.whiskering UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.PrecategoryBinProduct UniMath.CategoryTheory.PointedFunctors UniMath.CategoryTheory.PointedFunctorsComposition UniMath.SubstitutionSystems.Signatures UniMath.SubstitutionSystems.Notation UniMath.CategoryTheory.Chains.Chains UniMath.CategoryTheory.Chains.OmegaCocontFunctors UniMath.CategoryTheory.exponentials