Theorems · Theorem · algebraic geometry

AlgebraicGeometry.isClosedImmersion_iff_isAffineHom

∀ {X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y},
  AlgebraicGeometry.IsClosedImmersion f ↔
    AlgebraicGeometry.IsAffineHom f ∧
      ∀ (U : Y.Opens),
        AlgebraicGeometry.IsAffineOpen U →
          Function.Surjective ⇑(CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.Scheme.Hom.app f U))

Defined in: Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion
Cited by: 1 results in Mathlib
Foundations: Depth 221 from the axioms · uses propext, Classical.choice, Quot.sound

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

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AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.Hom.app_surjectiveproof · cited by 0