Theorems · Definition · category theory

CategoryTheory.leftDistrib

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v, u_1} C] →
    [inst_1 : CategoryTheory.MonoidalCategory C] →
      [inst_2 : CategoryTheory.Limits.HasBinaryCoproducts C] →
        [CategoryTheory.IsMonoidalLeftDistrib C] →
          (X Y Z : C) →
            CategoryTheory.MonoidalCategoryStruct.tensorObj X Y ⨿ CategoryTheory.MonoidalCategoryStruct.tensorObj X Z ≅
              CategoryTheory.MonoidalCategoryStruct.tensorObj X (Y ⨿ Z)

The canonical left distributivity isomorphism

Defined in

Mathlib.CategoryTheory.Distributive.Monoidal

Cited by

12 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Limits.HasBinaryCoproductsCategoryTheory.IsMonoidalLeftDistrib