Theorems · Theorem · category theory

CategoryTheory.Localization.Monoidal.triangle

∀ {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}
  (X Y : CategoryTheory.LocalizedMonoidal L W ε),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.associator X
          (CategoryTheory.MonoidalCategoryStruct.tensorUnit (CategoryTheory.LocalizedMonoidal L W ε)) Y).hom
      (CategoryTheory.MonoidalCategoryStruct.whiskerLeft X (CategoryTheory.MonoidalCategoryStruct.leftUnitor Y).hom) =
    CategoryTheory.MonoidalCategoryStruct.whiskerRight (CategoryTheory.MonoidalCategoryStruct.rightUnitor X).hom Y

Defined in

Mathlib.CategoryTheory.Localization.Monoidal.Basic

Cited by

0 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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