Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.MonoidalLeftAction.whiskerRight_actionHomLeft

∀ {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'' : C) (f : c ⟶ c') (d : D),
  CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHomLeft
      (CategoryTheory.MonoidalCategoryStruct.whiskerRight f c'') d =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionAssocIso c c'' d).hom
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHomLeft f
          (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionObj c'' d))
        (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionAssocIso c' c'' d).inv)

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