Theorems · Definition · category theory

CategoryTheory.CartesianMonoidalCategory.prodComparisonNatIso

{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 : C) →
                [∀ (B : C), CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.pair A B) F] →
                  ((CategoryTheory.MonoidalCategory.curriedTensor C).obj A).comp F ≅
                    F.comp ((CategoryTheory.MonoidalCategory.curriedTensor D).obj (F.obj A))

The natural isomorphism F(A ⊗ -) ≅ FA ⊗ F-, provided each prodComparison F A B is an isomorphism (as B changes).

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.Basic

Cited by

7 results in Mathlib

Foundations

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

Assumes

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