Theorems · Theorem · category theory

CategoryTheory.Mathlib.Tactic.MonTauto.add_assoc_hom_assoc

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C] {M X : C}
  [inst_2 : CategoryTheory.AddMonObj M] (f : X ⟶ M) {Z : C} (h : M ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator X M M).hom
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.tensorHom f CategoryTheory.AddMonObj.add)
        (CategoryTheory.CategoryStruct.comp CategoryTheory.AddMonObj.add h)) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.tensorHom
        (CategoryTheory.CategoryStruct.comp
          (CategoryTheory.MonoidalCategoryStruct.tensorHom f (CategoryTheory.CategoryStruct.id M))
          CategoryTheory.AddMonObj.add)
        (CategoryTheory.CategoryStruct.id M))
      (CategoryTheory.CategoryStruct.comp CategoryTheory.AddMonObj.add h)

Defined in

Mathlib.CategoryTheory.Monoidal.Mon

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.AddMonObj