Theorems · Definition · category theory

CategoryTheory.Monad.comparisonForget

{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} → (h : L ⊣ R) → (CategoryTheory.Monad.comparison h).comp h.toMonad.forget ≅ R

The underlying object of (Monad.comparison R).obj X is just R.obj X.

Defined in

Mathlib.CategoryTheory.Monad.Adjunction

Cited by

2 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category