Theorems · Definition · algebraic geometry
AlgebraicGeometry.structureSheafInType
(R M : Type u) →
[inst : CommRing R] →
[inst_1 : AddCommGroup M] → [Module R M] → TopCat.Sheaf (Type u) (AlgebraicGeometry.PrimeSpectrum.Top R)The structure sheaf (valued in Type, not yet CommRingCat) is the subsheaf consisting of
functions satisfying isLocallyFraction.
- Defined in
- Mathlib.AlgebraicGeometry.StructureSheaf
- Cited by
- 59 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
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.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- AlgebraicGeometry.PrimeSpectrum.Topstatement · cited by 104
- TopCat.Sheafstatement · cited by 73
- AlgebraicGeometry.StructureSheaf.isLocallyFractionproof · cited by 8
- TopCat.subsheafToTypesproof · cited by 5
Cited by71
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.structurePresheafInCommRingCatproof · cited by 23
- AlgebraicGeometry.StructureSheaf.toStalkproof · cited by 21
- AlgebraicGeometry.StructureSheaf.conststatement · cited by 20
- AlgebraicGeometry.StructureSheaf.comapproof · cited by 15
- AlgebraicGeometry.toSpecΓproof · cited by 8
- AlgebraicGeometry.StructureSheaf.algebraMap_germstatement and proof · cited by 6
- AlgebraicGeometry.StructureSheaf.comapₗstatement and proof · cited by 3
- AlgebraicGeometry.StructureSheaf.toPushforwardStalkproof · cited by 3
- AlgebraicGeometry.LocallyRingedSpace.toΓSpecSheafedSpace_app_specstatement · cited by 3
- AlgebraicGeometry.Spec.sheafedSpaceMap_hom_c_appstatement · cited by 2
- AlgebraicGeometry.StructureSheaf.algebraMap_self_mapstatement · cited by 2
- AlgebraicGeometry.StructureSheaf.const_algebraMapstatement · cited by 2