proposition: Theorem functorBinaryProduct {B C:category} : BinaryProducts C -> BinaryProducts [B,C].
proof: Proof. intros prod F G. unshelve refine (z_iso_Representation_weq _ _). { exact (bifunctor_assoc (binaryProductFunctor F G)). } { now apply BinaryProductFunctorAssoc. } { apply bifunctor_assoc_repn. intro b. apply prod. } 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