Theorems · Definition · category theory

CategoryTheory.leftDistributor

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      [inst_2 : CategoryTheory.MonoidalCategory C] →
        [CategoryTheory.MonoidalPreadditive C] →
          [inst_4 : CategoryTheory.Limits.HasFiniteBiproducts C] →
            {J : Type} →
              [inst_5 : Finite J] →
                (X : C) →
                  (f : J → C) →
                    CategoryTheory.MonoidalCategoryStruct.tensorObj X (⨁ f) ≅
                      ⨁ fun j => CategoryTheory.MonoidalCategoryStruct.tensorObj X (f j)

The isomorphism showing how tensor product on the left distributes over direct sums.

Defined in

Mathlib.CategoryTheory.Monoidal.Preadditive

Cited by

15 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalPreadditiveCategoryTheory.Limits.HasFiniteBiproductsFinite