Theorems · Definition · category theory

CompHausLike.LocallyConstant.counit

(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] →
              ((CategoryTheory.sheafSections (CategoryTheory.coherentTopology (CompHausLike P)) (Type (max u w))).obj
                      (Opposite.op (CompHausLike.of P PUnit.{u + 1}))).comp
                  (CompHausLike.LocallyConstant.functor P hs) ⟶
                CategoryTheory.Functor.id
                  (CategoryTheory.Sheaf (CategoryTheory.coherentTopology (CompHausLike P)) (Type (max u w)))

The counit is natural in both S : CompHausLike P and Y : Sheaf (coherentTopology (CompHausLike P)) (Type (max u w))

Defined in

Mathlib.Condensed.Discrete.LocallyConstant

Cited by

4 results in Mathlib

Foundations

Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CompHausLike.HasPropCompHausLike.HasPropCompHausLike.HasExplicitFiniteCoproductsCompHausLike.HasExplicitPullbacksCompHausLike.HasExplicitFiniteCoproducts