Theorems · Theorem · category theory

CategoryTheory.whiskerRight_coprod_inr_rightDistrib_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.IsMonoidalRightDistrib C] {X Y Z : C},
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerRight CategoryTheory.Limits.coprod.inr X) (∂R X Y Z).inv =
    CategoryTheory.Limits.coprod.inr

The composite of (coprod.inr ▷ X) : Z ⊗ X ⟶ (Y ⨿ Z) ⊗ X and (∂R X Y Z).inv : (Y ⨿ Z) ⊗ X ⟶ (Y ⊗ X) ⨿ (Z ⊗ X) is equal to the right coprojection coprod.inr : Z ⊗ X ⟶ (Y ⊗ X) ⨿ (Z ⊗ X).

Defined in

Mathlib.CategoryTheory.Distributive.Monoidal

Cited by

1 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Limits.HasBinaryCoproductsCategoryTheory.IsMonoidalRightDistrib