Theorems · Theorem · algebraic geometry
AlgebraicGeometry.HasRingHomProperty.of_isZariskiLocalAtSource_of_isZariskiLocalAtTarget
∀ (P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme) [AlgebraicGeometry.IsZariskiLocalAtTarget P]
[AlgebraicGeometry.IsZariskiLocalAtSource P],
AlgebraicGeometry.HasRingHomProperty P fun {R S} [CommRing R] [CommRing S] f =>
P (AlgebraicGeometry.Spec.map (CommRingCat.ofHom f))- Cited by
- 2 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homproof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- TopCat.carrierproof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatproof · cited by 2,333
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- AlgebraicGeometry.Scheme.toLocallyRingedSpaceproof · cited by 1,734
- CategoryTheory.PreZeroHypercover.I₀proof · cited by 763
- CategoryTheory.PreZeroHypercover.Xproof · cited by 649
- AlgebraicGeometry.Specstatement and proof · cited by 626
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Flat.generalizingMapproof · cited by 0
- AlgebraicGeometry.HasRingHomProperty.stalkwiseproof · cited by 0