Mathlib Map

Theorems · Theorem · algebraic geometry

AlgebraicGeometry.IsPreimmersion.mk_SpecMap

∀ {R S : CommRingCat} {f : R ⟶ S},
  Topology.IsEmbedding (PrimeSpectrum.comap (CommRingCat.Hom.hom f)) →
    (CommRingCat.Hom.hom f).SurjectiveOnStalks → AlgebraicGeometry.IsPreimmersion (AlgebraicGeometry.Spec.map f)
Defined in
Mathlib.AlgebraicGeometry.Morphisms.Preimmersion
Cited by
1 results in Mathlib
Foundations
Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AlgebraicGeometry.IsPreimmersion.of_isLocalization · cited by 0IsPreimmersion.of_isLocal…Quiver.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.IsPreimmersion · cited by 14AlgebraicGeometry.IsPreim…AlgebraicGeometry.IsPreimmersion.SpecMap_iff · cited by 1IsPreimmersion.SpecMap_iffIsPreimmersion.mk_SpecMapCITED BYCITES

Cites12

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

Cited by1

Results whose statement or proof uses this declaration.