Theorems · Definition · category theory

CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedActionActionOfMonoidalFunctorToEndofunctorIso

{C : Type u_1} →
  {D : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.MonoidalCategory C] →
        [inst_2 : CategoryTheory.Category.{v_2, u_2} D] →
          (F : CategoryTheory.Functor C (CategoryTheory.Functor D D)) →
            [inst_3 : F.Monoidal] → CategoryTheory.MonoidalCategory.MonoidalRightAction.curriedAction C D ≅ F

If the action of C on D comes from a monoidal functor C ⥤ (D ⥤ D), then curriedActionMop C D is naturally isomorphic to that functor.

Defined in

Mathlib.CategoryTheory.Monoidal.Action.End

Cited by

2 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.Functor.Monoidal