Theorems · Theorem · category theory

CategoryTheory.Mathlib.Tactic.MonTauto.mul_assoc_inv

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C] {M X : C}
  [inst_2 : CategoryTheory.MonObj M] (f : X ⟶ M),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator M M X).inv
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.tensorHom CategoryTheory.MonObj.mul f)
        CategoryTheory.MonObj.mul) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.tensorHom (CategoryTheory.CategoryStruct.id M)
        (CategoryTheory.CategoryStruct.comp
          (CategoryTheory.MonoidalCategoryStruct.tensorHom (CategoryTheory.CategoryStruct.id M) f)
          CategoryTheory.MonObj.mul))
      CategoryTheory.MonObj.mul

Defined in

Mathlib.CategoryTheory.Monoidal.Mon

Cited by

3 results in Mathlib

Foundations

Depth 9 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonObj