Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.MonoidalLeftAction.action_exchange_assoc

∀ {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]
  [inst_3 : CategoryTheory.MonoidalCategory.MonoidalLeftAction C D] {w x : C} {y z : D} (f : w ⟶ x) (g : y ⟶ z) {Z : D}
  (h : CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionObj x z ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHomRight w g)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHomLeft f z)
        h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHomLeft f y)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHomRight x g)
        h)

Defined in

Mathlib.CategoryTheory.Monoidal.Action.Basic

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalCategory.MonoidalLeftAction