Theorems · Definition · category theory

CategoryTheory.Monad.MonadicityInternal.counitCoequalizerOfReflectsCoequalizer

{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) →
              (B : D) →
                [CategoryTheory.Limits.ReflectsColimit
                      (CategoryTheory.Limits.parallelPair (F.map (G.map (adj.counit.app B)))
                        (adj.counit.app (F.obj (G.obj B))))
                      G] →
                  CategoryTheory.Limits.IsColimit (CategoryTheory.Monad.MonadicityInternal.counitCofork adj B)

The counit cofork is a colimit provided G reflects it.

Defined in

Mathlib.CategoryTheory.Monad.Monadicity

Cited by

0 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.ReflectsColimit