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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.IsPreimmersion.SpecMap_iff

∀ {R S : CommRingCat} (f : R ⟶ S),
  AlgebraicGeometry.IsPreimmersion (AlgebraicGeometry.Spec.map f) ↔
    Topology.IsEmbedding (PrimeSpectrum.comap (CommRingCat.Hom.hom f)) ∧ (CommRingCat.Hom.hom f).SurjectiveOnStalks
Defined in
Mathlib.AlgebraicGeometry.Morphisms.Preimmersion
Cited by
1 results in Mathlib
Foundations
Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.IsPreimmersion.mk_SpecMap · cited by 1IsPreimmersion.mk_SpecMapQuiver.Hom · cited by 32603Quiver.HomCommRingCat · cited by 2333CommRingCatCommRingCat.carrier · cited by 1096CommRingCat.carrierAlgebraicGeometry.Spec · cited by 626AlgebraicGeometry.SpecPrimeSpectrum · cited by 625PrimeSpectrumCommRingCat.Hom.hom · cited by 432Hom.homAlgebraicGeometry.Spec.map · cited by 332Spec.mapTopology.IsEmbedding · cited by 294Topology.IsEmbeddingPrimeSpectrum.comap · cited by 199PrimeSpectrum.comapRingHom.SurjectiveOnStalks · cited by 26RingHom.SurjectiveOnStalksAlgebraicGeometry.HasRingHomProperty.Spec_iff · cited by 19HasRingHomProperty.Spec_i…AlgebraicGeometry.SurjectiveOnStalks · cited by 16AlgebraicGeometry.Surject…AlgebraicGeometry.IsPreimmersion · cited by 14AlgebraicGeometry.IsPreim…AlgebraicGeometry.isPreimmersion_iff · cited by 3AlgebraicGeometry.isPreim…IsPreimmersion.SpecMap_iffCITED BYCITES

Cites14

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