Theorems · Theorem · category theory

CategoryTheory.Monad.MonadicityInternal.comparisonAdjunction_unit_f_aux

∀ {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))]
  (A : adj.toMonad.Algebra),
  ((CategoryTheory.Monad.MonadicityInternal.comparisonAdjunction adj).unit.app A).f =
    (adj.homEquiv A.A (CategoryTheory.Limits.coequalizer (F.map A.a) (adj.counit.app (F.obj A.A))))
      (CategoryTheory.Limits.coequalizer.π (F.map A.a) (adj.counit.app (F.obj A.A)))

Defined in

Mathlib.CategoryTheory.Monad.Monadicity

Cited by

1 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasCoequalizer