Theorems · Definition · category theory

CategoryTheory.Adjunction.toMonad

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {L : CategoryTheory.Functor C D} → {R : CategoryTheory.Functor D C} → (L ⊣ R) → CategoryTheory.Monad C

For a pair of functors L : C ⥤ D, R : D ⥤ C, an adjunction h : L ⊣ R induces a monad on the category C.

Defined in

Mathlib.CategoryTheory.Monad.Adjunction

Cited by

22 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category