Theorems · Definition · category theory

CompHausLike.LocallyConstant.adjunction

(P : TopCat → Prop) →
  [∀ (S : CompHausLike P) (p : ↑S.toTop → Prop), CompHausLike.HasProp P (Subtype p)] →
    [inst : CompHausLike.HasProp P PUnit.{u + 1}] →
      [inst_1 : CompHausLike.HasExplicitFiniteCoproducts P] →
        [inst_2 : CompHausLike.HasExplicitPullbacks P] →
          (hs :
              ∀ ⦃X Y : CompHausLike P⦄ (f : X ⟶ Y),
                CategoryTheory.EffectiveEpi f → Function.Surjective ⇑(CategoryTheory.ConcreteCategory.hom f)) →
            [CompHausLike.HasExplicitFiniteCoproducts P] →
              CompHausLike.LocallyConstant.functor P hs ⊣
                (CategoryTheory.sheafSections (CategoryTheory.coherentTopology (CompHausLike P)) (Type (max u w))).obj
                  (Opposite.op (CompHausLike.of P PUnit.{u + 1}))

CompHausLike.LocallyConstant.functor is left adjoint to the forgetful functor.

Defined in

Mathlib.Condensed.Discrete.LocallyConstant

Cited by

2 results in Mathlib

Foundations

Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CompHausLike.HasPropCompHausLike.HasPropCompHausLike.HasExplicitFiniteCoproductsCompHausLike.HasExplicitPullbacksCompHausLike.HasExplicitFiniteCoproducts