Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionAssocIso_hom_naturality

∀ {C : Type u_1} {D : Type u_2} {inst : CategoryTheory.Category.{v_1, u_1} C}
  {inst_1 : CategoryTheory.Category.{v_2, u_2} D} {inst_2 : CategoryTheory.MonoidalCategory C}
  [self : CategoryTheory.MonoidalCategory.MonoidalLeftAction C D] {c₁ c₂ c₃ c₄ : C} {d₁ d₂ : D} (f : c₁ ⟶ c₂)
  (g : c₃ ⟶ c₄) (h : d₁ ⟶ d₂),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHom
        (CategoryTheory.MonoidalCategoryStruct.tensorHom f g) h)
      (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionAssocIso c₂ c₄ d₂).hom =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionAssocIso c₁ c₃ d₁).hom
      (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHom f
        (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHom g h))

Defined in

Mathlib.CategoryTheory.Monoidal.Action.Basic

Cited by

3 results in Mathlib

Foundations

Depth 5 from the axioms · uses no axioms

Assumes

CategoryTheory.MonoidalCategory.MonoidalLeftAction