Theorems · Inductive type · category theory

CategoryTheory.MonadicRightAdjoint

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

A right adjoint functor R : D ⥤ C is monadic if the comparison functor Monad.comparison R from D to the category of Eilenberg-Moore algebras for the adjunction is an equivalence.

Defined in

Mathlib.CategoryTheory.Monad.Adjunction

Cited by

2 results in Mathlib

Foundations

Depth 2 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category