Theorems · Definition · algebraic geometry
AlgebraicGeometry.stalkwise
({R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop) →
CategoryTheory.MorphismProperty AlgebraicGeometry.Schemestalkwise P holds for a morphism if all stalks satisfy P.
- 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.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homproof · cited by 32,603
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TopCat.carrierproof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.MorphismPropertystatement · cited by 2,179
- AlgebraicGeometry.PresheafedSpace.carrierproof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpaceproof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpaceproof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpaceproof · cited by 1,734
Cited by8
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.stalkwise_SpecMap_iffstatement · cited by 2
- AlgebraicGeometry.stalkwise_respectsIsostatement · cited by 2
- AlgebraicGeometry.isOpenImmersion_eq_infstatement and proof · cited by 1
- AlgebraicGeometry.SurjectiveOnStalks.eq_stalkwisestatement · cited by 1
- AlgebraicGeometry.stalkwiseIsZariskiLocalAtTarget_of_respectsIsostatement and proof · cited by 1
- AlgebraicGeometry.stalkwise_isZariskiLocalAtSource_of_respectsIsostatement and proof · cited by 1
- AlgebraicGeometry.isomorphisms_eq_stalkwisestatement and proof · cited by 0
- AlgebraicGeometry.HasRingHomProperty.stalkwisestatement and proof · cited by 0