Theorems · Theorem · algebraic geometry

AlgebraicGeometry.IsClosedImmersion.Spec_iff

∀ {X : AlgebraicGeometry.Scheme} {R : CommRingCat} {f : X ⟶ AlgebraicGeometry.Spec R},
  AlgebraicGeometry.IsClosedImmersion f ↔
    ∃ I e,
      f =
        CategoryTheory.CategoryStruct.comp e.hom (AlgebraicGeometry.Spec.map (CommRingCat.ofHom (Ideal.Quotient.mk I)))

Defined in: Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion
Cited by: 1 results in Mathlib
Foundations: Depth 220 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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Cited by1

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AlgebraicGeometry.isIso_of_comp_eq_sigmaSpecproof · cited by 1