Theorems · Theorem · category theory

CategoryTheory.whiskerRight_coprod_inl_rightDistrib_inv_assoc

∀ {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 Z_1 : C}
  (h : CategoryTheory.MonoidalCategoryStruct.tensorObj Y X ⨿ CategoryTheory.MonoidalCategoryStruct.tensorObj Z X ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerRight CategoryTheory.Limits.coprod.inl X)
      (CategoryTheory.CategoryStruct.comp (∂R X Y Z).inv h) =
    CategoryTheory.CategoryStruct.comp CategoryTheory.Limits.coprod.inl h

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

Defined in

Mathlib.CategoryTheory.Distributive.Monoidal

Cited by

0 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Limits.HasBinaryCoproductsCategoryTheory.IsMonoidalRightDistrib