Theorems · Theorem · category theory

CategoryTheory.MonObj.mul_associator

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.BraidedCategory C] {M N P : C} [inst_3 : CategoryTheory.MonObj M]
  [inst_4 : CategoryTheory.MonObj N] [inst_5 : CategoryTheory.MonObj P],
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategory.tensorμ (CategoryTheory.MonoidalCategoryStruct.tensorObj M N) P
          (CategoryTheory.MonoidalCategoryStruct.tensorObj M N) P)
        (CategoryTheory.MonoidalCategoryStruct.tensorHom
          (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategory.tensorμ M N M N)
            (CategoryTheory.MonoidalCategoryStruct.tensorHom CategoryTheory.MonObj.mul CategoryTheory.MonObj.mul))
          CategoryTheory.MonObj.mul))
      (CategoryTheory.MonoidalCategoryStruct.associator M N P).hom =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.tensorHom (CategoryTheory.MonoidalCategoryStruct.associator M N P).hom
        (CategoryTheory.MonoidalCategoryStruct.associator M N P).hom)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategory.tensorμ M (CategoryTheory.MonoidalCategoryStruct.tensorObj N P) M
          (CategoryTheory.MonoidalCategoryStruct.tensorObj N P))
        (CategoryTheory.MonoidalCategoryStruct.tensorHom CategoryTheory.MonObj.mul
          (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategory.tensorμ N P N P)
            (CategoryTheory.MonoidalCategoryStruct.tensorHom CategoryTheory.MonObj.mul CategoryTheory.MonObj.mul))))

Defined in

Mathlib.CategoryTheory.Monoidal.Mon

Cited by

0 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.MonObjCategoryTheory.MonObjCategoryTheory.MonObj