Theorems · Theorem · category theory

CategoryTheory.Localization.Monoidal.whisker_exchange_assoc

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] (L : CategoryTheory.Functor C D)
  (W : CategoryTheory.MorphismProperty C) [inst_2 : CategoryTheory.MonoidalCategory C] [inst_3 : W.IsMonoidal]
  [inst_4 : L.IsLocalization W] {unit : D} (ε : L.obj (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) ≅ unit)
  {Q X Y Z : CategoryTheory.LocalizedMonoidal L W ε} (f : Q ⟶ X) (g : Y ⟶ Z)
  {Z_1 : CategoryTheory.LocalizedMonoidal L W ε} (h : CategoryTheory.MonoidalCategoryStruct.tensorObj X Z ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft Q g)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight f Z) h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight f Y)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft X g) h)

Defined in

Mathlib.CategoryTheory.Localization.Monoidal.Basic

Cited by

1 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MorphismProperty.IsMonoidalCategoryTheory.Functor.IsLocalization