proposition: Proposition cartesian_tensor_mor {x₁ x₂ y₁ y₂ : M} (f : x₁ --> x₂) (g : y₁ --> y₂) : f #⊗ g = BinProductOfArrows _ (is_cartesian_BinProduct M_cart x₂ y₂) (is_cartesian_BinProduct M_cart x₁ y₁) f g.
proof: Proof. use (BinProductArrowsEq _ _ _ (is_cartesian_BinProduct M_cart _ _)). - refine (!_). etrans. { apply (BinProductOfArrowsPr1 _ (is_cartesian_BinProduct M_cart x₂ y₂) (is_cartesian_BinProduct M_cart x₁ y₁)). } cbn. rewrite cartesian_tensor_pr1. apply idpath. - refine (!_). etrans. { apply (BinProductOfArrowsPr2 _ (is_cartesian_BinProduct M_cart x₂ y₂) (is_cartesian_BinProduct M_cart x₁ y₁)). } cbn. rewrite cartesian_tensor_pr2. apply idpath. Qed.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.CategoryTheory.Core.Categories UniMath.CategoryTheory.Core.Isos UniMath.CategoryTheory.Core.Functors UniMath.CategoryTheory.Core.NaturalTransformations UniMath.CategoryTheory.Adjunctions.Core UniMath.CategoryTheory.Monoidal.WhiskeredBifunctors UniMath.CategoryTheory.Monoidal.Categories UniMath.CategoryTheory.Monoidal.Structure.Symmetric UniMath.CategoryTheory.Limits.Terminal UniMath.CategoryTheory.Limits.BinProducts UniMath.CategoryTheory.Limits.Initial UniMath.CategoryTheory.Limits.BinCoproducts