Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Spec.map_surjective
∀ {R S : CommRingCat}, Function.Surjective AlgebraicGeometry.Spec.mapUseful for replacing f by Spec.map φ everywhere in proofs.
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- AlgebraicGeometry.Schemestatement · cited by 2,540
- CommRingCatstatement and proof · cited by 2,333
- AlgebraicGeometry.Specstatement and proof · cited by 626
- AlgebraicGeometry.Spec.mapstatement · cited by 332
- AlgebraicGeometry.Spec.preimageproof · cited by 14
- AlgebraicGeometry.Spec.map_preimageproof · cited by 11
Cited by25
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.support_kerproof · cited by 6
- AlgebraicGeometry.IsZariskiLocalAtTarget.descendsAlong_inf_quasiCompactproof · cited by 2
- AlgebraicGeometry.LocallyOfFiniteType.isLocallyNoetherianproof · cited by 2
- AlgebraicGeometry.LocallyQuasiFinite.of_fiberToSpecResidueFieldproof · cited by 2
- AlgebraicGeometry.LocallyQuasiFinite.of_finite_preimage_singletonproof · cited by 2
- AlgebraicGeometry.HasRingHomProperty.stalkMap_of_respectsIsoproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.quasiFiniteAt_iff_isOpen_singleton_asFiberproof · cited by 2
- AlgebraicGeometry.IsLocallyArtinian.of_locallyQuasiFiniteproof · cited by 2
- AlgebraicGeometry.of_pullback_fst_Spec_of_codescendsAlongproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.one_le_finrank_mapproof · cited by 1
- AlgebraicGeometry.locallyQuasiFinite_iff_isDiscrete_preimage_singletonproof · cited by 1
- AlgebraicGeometry.Flat.isQuotientMap_of_surjectiveproof · cited by 1