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Theorems · Definition · algebraic geometry

AlgebraicGeometry.structurePresheafInCommRingCat

(R : Type u) → [inst : CommRing R] → TopCat.Presheaf CommRingCat (AlgebraicGeometry.PrimeSpectrum.Top R)

The structure presheaf, valued in CommRingCat, constructed by dressing up the Type-valued structure presheaf.

Defined in
Mathlib.AlgebraicGeometry.StructureSheaf
Cited by
23 results in Mathlib
Foundations
Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRing
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AlgebraicGeometry.Spec.structureSheaf · cited by 57Spec.structureSheafAlgebraicGeometry.StructureSheaf.toStalk · cited by 21StructureSheaf.toStalkAlgebraicGeometry.StructureSheaf.algebraMap_germ · cited by 6StructureSheaf.algebraMap…AlgebraicGeometry.basicOpen_eq_of_affine · cited by 5AlgebraicGeometry.basicOp…AlgebraicGeometry.StructureSheaf.stalkIso · cited by 5StructureSheaf.stalkIsoAlgebraicGeometry.localRingHom_comp_stalkIso · cited by 3AlgebraicGeometry.localRi…AlgebraicGeometry.StructureSheaf.toStalk_stalkSpecializes · cited by 2StructureSheaf.toStalk_st…AlgebraicGeometry.Spec.fromSpecStalk_eq' · cited by 2Spec.fromSpecStalk_eq'AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp · cited by 1StructureSheaf.toPushforw…AlgebraicGeometry.ProjectiveSpectrum.Proj.toStalk_specStalkEquiv · cited by 1Proj.toStalk_specStalkEqu…AlgebraicGeometry.ValuativeCriterion.Existence.of_specializingMap · cited by 1Existence.of_specializing…AlgebraicGeometry.stalkMap_toStalk · cited by 1AlgebraicGeometry.stalkMa…AlgebraicGeometry.stalkMap_toStalk_apply · cited by 1AlgebraicGeometry.stalkMa…AlgebraicGeometry.localRingHom_comp_stalkIso_apply · cited by 0AlgebraicGeometry.localRi…AlgebraicGeometry.StructureSheaf.toPushforwardStalk_comp_assoc · cited by 0StructureSheaf.toPushforw…DFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCommRing · cited by 17173CommRingCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homTopCat.carrier · cited by 3184TopCat.carrierCommRingCat · cited by 2333CommRingCatTopologicalSpace.Opens · cited by 2040TopologicalSpace.OpensCategoryTheory.ObjectProperty.FullSubcategory.obj · cited by 1316FullSubcategory.objTopCat.Presheaf · cited by 371TopCat.PresheafCommRingCat.ofHom · cited by 259CommRingCat.ofHomAlgebraicGeometry.PrimeSpectrum.Top · cited by 104PrimeSpectrum.TopAlgebraicGeometry.structureSheafInType · cited by 59AlgebraicGeometry.structu…AlgebraicGeometry.structurePr…CITED BYCITES

Cites15

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Cited by30

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