Theorems · Definition · category theory

CategoryTheory.Functor.Monoidal.tensorObjComp

{C : Type u_2} →
  {D : Type u_3} →
    {E : Type u_4} →
      [inst : CategoryTheory.Category.{v_2, u_2} C] →
        [inst_1 : CategoryTheory.Category.{v_3, u_3} D] →
          [inst_2 : CategoryTheory.Category.{v_4, u_4} E] →
            [inst_3 : CategoryTheory.CartesianMonoidalCategory C] →
              [inst_4 : CategoryTheory.CartesianMonoidalCategory E] →
                (F G : CategoryTheory.Functor D C) →
                  (H : CategoryTheory.Functor C E) →
                    [CategoryTheory.Limits.PreservesFiniteProducts H] →
                      (CategoryTheory.MonoidalCategoryStruct.tensorObj F G).comp H ≅
                        CategoryTheory.MonoidalCategoryStruct.tensorObj (F.comp H) (G.comp H)

A finite-products-preserving functor distributes over the tensor product of functors.

Defined in

Mathlib.CategoryTheory.Monoidal.Cartesian.FunctorCategory

Cited by

2 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.Limits.PreservesFiniteProducts