Theorems · Definition · category theory

CategoryTheory.Comonad.ComonadicityInternal.counitLimitOfPreservesEqualizer

{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) →
                [inst_2 : CategoryTheory.Limits.HasEqualizer (G.map A.a) (adj.unit.app (G.obj A.A))] →
                  [CategoryTheory.Limits.PreservesLimit
                        (CategoryTheory.Limits.parallelPair (G.map A.a) (adj.unit.app (G.obj A.A))) F] →
                    CategoryTheory.Limits.IsLimit (CategoryTheory.Comonad.ComonadicityInternal.counitFork A)

The counit fork is a limit provided F preserves it.

Defined in

Mathlib.CategoryTheory.Monad.Comonadicity

Cited by

0 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasEqualizerCategoryTheory.Limits.PreservesLimit