Theorems · Definition · category theory

CategoryTheory.Monad.MonadicityInternal.comparisonAdjunction

{C : Type u₁} →
  {D : Type u₂} →
    [inst : CategoryTheory.Category.{v₁, u₁} C] →
      [inst_1 : CategoryTheory.Category.{v₁, u₂} D] →
        {G : CategoryTheory.Functor D C} →
          {F : CategoryTheory.Functor C D} →
            (adj : F ⊣ G) →
              [inst_2 :
                  ∀ (A : adj.toMonad.Algebra),
                    CategoryTheory.Limits.HasCoequalizer (F.map A.a) (adj.counit.app (F.obj A.A))] →
                CategoryTheory.Monad.MonadicityInternal.leftAdjointComparison adj ⊣ CategoryTheory.Monad.comparison adj

Provided we have the appropriate coequalizers, we have an adjunction to the comparison functor.

Defined in

Mathlib.CategoryTheory.Monad.Monadicity

Cited by

4 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasCoequalizer