Theorems · Definition · category theory

CompHausLike.LocallyConstant.functorIso

(P : TopCat → Prop) →
  [inst : CompHausLike.HasExplicitFiniteCoproducts P] →
    [inst_1 : CompHausLike.HasExplicitPullbacks P] →
      (hs :
          ∀ ⦃X Y : CompHausLike P⦄ (f : X ⟶ Y),
            CategoryTheory.EffectiveEpi f → Function.Surjective ⇑(CategoryTheory.ConcreteCategory.hom f)) →
        CompHausLike.LocallyConstant.functor P hs ≅ TopCat.discrete.comp (topCatToSheafCompHausLike P hs)

CompHausLike.LocallyConstant.functor is naturally isomorphic to the restriction of topCatToSheafCompHausLike to discrete topological spaces.

Defined in

Mathlib.Condensed.Discrete.LocallyConstant

Cited by

0 results in Mathlib

Foundations

Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CompHausLike.HasExplicitFiniteCoproductsCompHausLike.HasExplicitPullbacks