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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.IdealSheafData.map_ideal_basicOpen

∀ {X : AlgebraicGeometry.Scheme} (self : X.IdealSheafData) (U : ↑X.affineOpens)
  (f : ↑(X.presheaf.obj (Opposite.op ↑U))),
  Ideal.map (CommRingCat.Hom.hom (X.presheaf.map (CategoryTheory.homOfLE ⋯).op)) (self.ideal U) =
    self.ideal (X.affineBasicOpen f)

Also see AlgebraicGeometry.Scheme.IdealSheafData.map_ideal

Defined in
Mathlib.AlgebraicGeometry.IdealSheaf.Basic
Cited by
2 results in Mathlib
Foundations
Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
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AlgebraicGeometry.Scheme.IdealSheafData.map_ideal · cited by 5IdealSheafData.map_idealAlgebraicGeometry.Scheme.irreducibleComponentIdeal · cited by 2Scheme.irreducibleCompone…AlgebraicGeometry.Scheme.IdealSheafData.zeroLocus_inter_subset_supportSet · cited by 2IdealSheafData.zeroLocus_…Set · cited by 53352SetCategoryTheory.Functor.obj · cited by 19642Functor.objRingHom · cited by 10189RingHomCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeSet.Elem · cited by 7166Set.ElemIdeal · cited by 4748IdealTopCat.carrier · cited by 3184TopCat.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatTopologicalSpace.Opens · cited by 2040TopologicalSpace.OpensAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…Quiver.Hom.op · cited by 1948Hom.opAlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…IdealSheafData.map_ideal_basi…CITED BYCITES

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