Theorems · Definition · category theory

CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatTrans

{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) →
              (CategoryTheory.MonoidalCategory.curriedTensor C).comp
                  ((CategoryTheory.Functor.whiskeringRight C C D).obj F) ⟶
                F.comp
                  ((CategoryTheory.MonoidalCategory.curriedTensor D).comp
                    ((CategoryTheory.Functor.whiskeringLeft C D D).obj F))

The product comparison morphism from F(- ⊗ -) to F- ⊗ F-, whose components are given by prodComparison.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Basic

Cited by

4 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategory