Theorems · Definition · category theory

CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop

{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)ᴹᵒᵖ) →
            [F.Monoidal] → CategoryTheory.MonoidalCategory.MonoidalLeftAction C D

A monoidal functor F : C ⥤ (D ⥤ D)ᴹᵒᵖ can be thought of as a left action of C on D.

Defined in

Mathlib.CategoryTheory.Monoidal.Action.End

Cited by

10 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.Functor.Monoidal