Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionUnitIso_inv_naturality_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] {d d' : D} (f : d ⟶ d') {Z : D}
  (h :
    CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionObj
        (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) d' ⟶
      Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionUnitIso d).inv
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHomRight
          (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) f)
        h) =
    CategoryTheory.CategoryStruct.comp f
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionUnitIso d').inv h)

Defined in

Mathlib.CategoryTheory.Monoidal.Action.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalCategory.MonoidalLeftAction