Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.associator_monoidal

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.BraidedCategory C] (X₁ X₂ X₃ Y₁ Y₂ Y₃ : C),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategory.tensorμ (CategoryTheory.MonoidalCategoryStruct.tensorObj X₁ X₂) X₃
        (CategoryTheory.MonoidalCategoryStruct.tensorObj Y₁ Y₂) Y₃)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.whiskerRight (CategoryTheory.MonoidalCategory.tensorμ X₁ X₂ Y₁ Y₂)
          (CategoryTheory.MonoidalCategoryStruct.tensorObj X₃ Y₃))
        (CategoryTheory.MonoidalCategoryStruct.associator (CategoryTheory.MonoidalCategoryStruct.tensorObj X₁ Y₁)
            (CategoryTheory.MonoidalCategoryStruct.tensorObj X₂ Y₂)
            (CategoryTheory.MonoidalCategoryStruct.tensorObj X₃ Y₃)).hom) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.tensorHom (CategoryTheory.MonoidalCategoryStruct.associator X₁ X₂ X₃).hom
        (CategoryTheory.MonoidalCategoryStruct.associator Y₁ Y₂ Y₃).hom)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategory.tensorμ X₁ (CategoryTheory.MonoidalCategoryStruct.tensorObj X₂ X₃) Y₁
          (CategoryTheory.MonoidalCategoryStruct.tensorObj Y₂ Y₃))
        (CategoryTheory.MonoidalCategoryStruct.whiskerLeft (CategoryTheory.MonoidalCategoryStruct.tensorObj X₁ Y₁)
          (CategoryTheory.MonoidalCategory.tensorμ X₂ X₃ Y₂ Y₃)))

Defined in

Mathlib.CategoryTheory.Monoidal.Braided.Basic

Cited by

3 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategory