Theorems · Theorem · category theory

CategoryTheory.MonObj.Mon_tensor_mul_assoc

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