Theorems · Definition · category theory

CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointHomEquiv

{C : Type u₁} →
  {D : Type u₂} →
    [inst : CategoryTheory.Category.{v₁, u₁} C] →
      [inst_1 : CategoryTheory.Category.{v₁, u₂} D] →
        {F : CategoryTheory.Functor C D} →
          {G : CategoryTheory.Functor D C} →
            (adj : F ⊣ G) →
              (A : adj.toComonad.Coalgebra) →
                (B : C) →
                  [inst_2 : CategoryTheory.Limits.HasEqualizer (G.map A.a) (adj.unit.app (G.obj A.A))] →
                    ((CategoryTheory.Comonad.comparison adj).obj B ⟶ A) ≃
                      (B ⟶ CategoryTheory.Comonad.ComonadicityInternal.comparisonRightAdjointObj adj A)

We have a bijection of homsets which will be used to construct the right adjoint to the comparison functor.

Defined in

Mathlib.CategoryTheory.Monad.Comonadicity

Cited by

4 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasEqualizer