Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomLeft_action

∀ {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] {x x' : C} (f : x ⟶ x') (y : C) (z : D),
  CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHomLeft f
      (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionObj y z) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionAssocIso x y z).inv
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHomLeft
          (CategoryTheory.MonoidalCategoryStruct.whiskerRight f y) z)
        (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionAssocIso x' y z).hom)

Defined in

Mathlib.CategoryTheory.Monoidal.Action.Basic

Cited by

1 results in Mathlib

Foundations

Depth 7 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalCategory.MonoidalLeftAction