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Theorems · Definition · algebraic geometry

AlgebraicGeometry.stalkwise

({R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop) →
  CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme

stalkwise P holds for a morphism if all stalks satisfy P.

Defined in
Mathlib.AlgebraicGeometry.Morphisms.Constructors
Cited by
8 results in Mathlib
Foundations
Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

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

AlgebraicGeometry.stalkwise_SpecMap_iff · cited by 2AlgebraicGeometry.stalkwi…AlgebraicGeometry.stalkwise_respectsIso · cited by 2AlgebraicGeometry.stalkwi…AlgebraicGeometry.isOpenImmersion_eq_inf · cited by 1AlgebraicGeometry.isOpenI…AlgebraicGeometry.SurjectiveOnStalks.eq_stalkwise · cited by 1SurjectiveOnStalks.eq_sta…AlgebraicGeometry.stalkwiseIsZariskiLocalAtTarget_of_respectsIso · cited by 1AlgebraicGeometry.stalkwi…AlgebraicGeometry.stalkwise_isZariskiLocalAtSource_of_respectsIso · cited by 1AlgebraicGeometry.stalkwi…AlgebraicGeometry.isomorphisms_eq_stalkwise · cited by 0AlgebraicGeometry.isomorp…AlgebraicGeometry.HasRingHomProperty.stalkwise · cited by 0HasRingHomProperty.stalkw…DFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomCommRing · cited by 17173CommRingRingHom · cited by 10189RingHomCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homTopCat.carrier · cited by 3184TopCat.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…AlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…AlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…AlgebraicGeometry.PresheafedSpace.Hom.base · cited by 1135Hom.baseAlgebraicGeometry.PresheafedSpace.presheaf · cited by 1104PresheafedSpace.presheafCommRingCat.carrier · cited by 1096CommRingCat.carrierAlgebraicGeometry.stalkwiseCITED BYCITES

Cites20

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Cited by8

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