Theorems · Theorem · category theory

CategoryTheory.CartesianMonoidalCategory.prodComparison_natural

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  {D : Type u₁} [inst_2 : CategoryTheory.Category.{v₁, u₁} D] [inst_3 : CategoryTheory.CartesianMonoidalCategory D]
  (F : CategoryTheory.Functor C D) {A B A' B' : C} (f : A ⟶ A') (g : B ⟶ B'),
  CategoryTheory.CategoryStruct.comp (F.map (CategoryTheory.MonoidalCategoryStruct.tensorHom f g))
      (CategoryTheory.CartesianMonoidalCategory.prodComparison F A' B') =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.CartesianMonoidalCategory.prodComparison F A B)
      (CategoryTheory.MonoidalCategoryStruct.tensorHom (F.map f) (F.map g))

Naturality of the prodComparison morphism in both arguments.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Basic

Cited by

2 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategory