Theorems · Theorem · category theory

CategoryTheory.whiskerLeft_coprod_inl_leftDistrib_inv

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v, u_1} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.Limits.HasBinaryCoproducts C] [inst_3 : CategoryTheory.IsMonoidalLeftDistrib C] {X Y Z : C},
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerLeft X CategoryTheory.Limits.coprod.inl)
      (CategoryTheory.leftDistrib X Y Z).inv =
    CategoryTheory.Limits.coprod.inl

The composite of (X ◁ coprod.inl) : X ⊗ Y ⟶ X ⊗ (Y ⨿ Z) and (∂L X Y Z).inv : X ⊗ (Y ⨿ Z) ⟶ (X ⊗ Y) ⨿ (X ⊗ Z) is equal to the left coprojection coprod.inl : X ⊗ Y ⟶ (X ⊗ Y) ⨿ (X ⊗ Z).

Defined in

Mathlib.CategoryTheory.Distributive.Monoidal

Cited by

2 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Limits.HasBinaryCoproductsCategoryTheory.IsMonoidalLeftDistrib