Theorems · Theorem · category theory

LightCondSet.epi_iff_locallySurjective_on_lightProfinite

∀ {X Y : LightCondSet} (f : X ⟶ Y),
  CategoryTheory.Epi f ↔
    ∀ (S : LightProfinite) (y : Y.obj.obj (Opposite.op S)),
      ∃ S' φ,
        ∃ (_ : Function.Surjective ⇑(CategoryTheory.ConcreteCategory.hom φ)),
          ∃ x,
            (CategoryTheory.ConcreteCategory.hom (f.hom.app (Opposite.op S'))) x =
              (CategoryTheory.ConcreteCategory.hom (Y.obj.map (Opposite.op φ))) y

Defined in

Mathlib.Condensed.Light.Epi

Cited by

1 results in Mathlib

Foundations

Depth 126 from the axioms · uses propext, Classical.choice, Quot.sound