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Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.Hom.toNormalization

{X Y : AlgebraicGeometry.Scheme} →
  (f : X ⟶ Y) →
    [inst : AlgebraicGeometry.QuasiCompact f] →
      [inst_1 : AlgebraicGeometry.QuasiSeparated f] → X ⟶ AlgebraicGeometry.Scheme.Hom.normalization f

The dominant morphism into the relative normalization.

Defined in
Mathlib.AlgebraicGeometry.Normalization
Cited by
28 results in Mathlib
Foundations
Depth 203 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.QuasiCompactAlgebraicGeometry.QuasiSeparated

Around this declaration

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

AlgebraicGeometry.Scheme.Hom.normalizationCoprodIso · cited by 15Hom.normalizationCoprodIsoAlgebraicGeometry.Scheme.Hom.toNormalization_fromNormalization · cited by 6Hom.toNormalization_fromN…AlgebraicGeometry.Scheme.Hom.normalizationPullback · cited by 5Hom.normalizationPullbackAlgebraicGeometry.Scheme.Hom.toNormalization_normalizationDesc · cited by 4Hom.toNormalization_norma…AlgebraicGeometry.Scheme.Hom.ι_toNormalization · cited by 2Hom.ι_toNormalizationAlgebraicGeometry.Scheme.Hom.ι_toNormalization_assoc · cited by 2Hom.ι_toNormalization_ass…AlgebraicGeometry.IsFinite.of_isProper_of_locallyQuasiFinite · cited by 2IsFinite.of_isProper_of_l…AlgebraicGeometry.Scheme.Hom.toNormalization_app_preimage · cited by 2Hom.toNormalization_app_p…AlgebraicGeometry.Scheme.Hom.toNormalization_normalizationDesc_assoc · cited by 2Hom.toNormalization_norma…AlgebraicGeometry.Scheme.Hom.toNormalization_normalizationPullback_fst · cited by 2Hom.toNormalization_norma…AlgebraicGeometry.Scheme.Hom.normalizationPullback_snd · cited by 2Hom.normalizationPullback…AlgebraicGeometry.Scheme.Hom.inl_toNormalization_normalizationCoprodIso_inv · cited by 1Hom.inl_toNormalization_n…AlgebraicGeometry.Scheme.Hom.inr_toNormalization_normalizationCoprodIso_inv · cited by 1Hom.inr_toNormalization_n…AlgebraicGeometry.Scheme.Hom.inr_normalizationCoprodIso_hom_fromNormalization · cited by 1Hom.inr_normalizationCopr…AlgebraicGeometry.Scheme.Hom.exists_isIso_morphismRestrict_toNormalization · cited by 1Hom.exists_isIso_morphism…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Iso.hom · cited by 7684Iso.homAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…AlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…AlgebraicGeometry.PresheafedSpace.Hom.base · cited by 1135Hom.baseAlgebraicGeometry.PresheafedSpace.presheaf · cited by 1104PresheafedSpace.presheafCommRingCat.carrier · cited by 1096CommRingCat.carrierAlgebraicGeometry.LocallyRingedSpace.Hom.toHom · cited by 995Hom.toHomAlgebraicGeometry.Scheme.Hom.toLRSHom' · cited by 895Hom.toLRSHom'CategoryTheory.PreZeroHypercover.I₀ · cited by 763PreZeroHypercover.I₀TopologicalSpace.Opens.map · cited by 645Opens.mapHom.toNormalizationCITED BYCITES

Cites32

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Cited by30

Results whose statement or proof uses this declaration.