Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHom_comp

∀ {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] {c c' c'' : C} {d d' d'' : D} (f₁ : c ⟶ c')
  (f₂ : c' ⟶ c'') (g₁ : d ⟶ d') (g₂ : d' ⟶ d''),
  CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHom (CategoryTheory.CategoryStruct.comp f₁ f₂)
      (CategoryTheory.CategoryStruct.comp g₁ g₂) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHom f₁ g₁)
      (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHom f₂ g₂)

Defined in: Mathlib.CategoryTheory.Monoidal.Action.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 5 from the axioms · uses no axioms
Assumes: CategoryTheory.MonoidalCategory.MonoidalLeftAction

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Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
CategoryTheory.MonoidalCategory.MonoidalLeftActionstatement and proof · cited by 215
CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionObjstatement · cited by 185
CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHomstatement · cited by 31

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHom_comp_assocproof · cited by 0