Theorems · Definition · category theory

CategoryTheory.CartesianMonoidalCategory.prodComparisonBifunctorNatIso

{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 : C), CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.pair A B) F] →
                (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 natural isomorphism of bifunctors F(- ⊗ -) ≅ F- ⊗ F-, provided each prodComparison F A B is an isomorphism.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Basic

Cited by

2 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.Limits.PreservesLimit