Mathlib Map

Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.Hom.fromNormalization

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

The morphism from the relative normalization to itself. This map is integral.

Defined in
Mathlib.AlgebraicGeometry.Normalization
Cited by
28 results in Mathlib
Foundations
Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.QuasiCompactAlgebraicGeometry.QuasiSeparated
Mathlib docsSourceLoogleLeanSearch

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.normalizationObjIso · cited by 6Hom.normalizationObjIsoAlgebraicGeometry.Scheme.Hom.normalizationDesc_comp · cited by 5Hom.normalizationDesc_compAlgebraicGeometry.Scheme.Hom.normalizationPullback · cited by 5Hom.normalizationPullbackAlgebraicGeometry.Scheme.Hom.ι_fromNormalization · cited by 4Hom.ι_fromNormalizationAlgebraicGeometry.Scheme.Hom.toNormalization_normalizationPullback_fst · cited by 2Hom.toNormalization_norma…AlgebraicGeometry.Scheme.Hom.toNormalization_app_preimage · cited by 2Hom.toNormalization_app_p…AlgebraicGeometry.Scheme.Hom.normalizationPullback_snd · cited by 2Hom.normalizationPullback…AlgebraicGeometry.Scheme.Hom.inr_normalizationCoprodIso_hom_fromNormalization · cited by 1Hom.inr_normalizationCopr…AlgebraicGeometry.Scheme.Hom.inl_normalizationCoprodIso_hom_fromNormalization · cited by 1Hom.inl_normalizationCopr…AlgebraicGeometry.Scheme.Hom.exists_isIso_morphismRestrict_toNormalization · cited by 1Hom.exists_isIso_morphism…AlgebraicGeometry.Scheme.Hom.exists_mem_and_isIso_morphismRestrict_toNormalization · cited by 1Hom.exists_mem_and_isIso_…AlgebraicGeometry.Scheme.Hom.fromNormalization_app · cited by 1Hom.fromNormalization_appAlgebraicGeometry.Scheme.Hom.fromNormalization_preimage · cited by 1Hom.fromNormalization_pre…Quiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.QuasiCompact · cited by 102AlgebraicGeometry.QuasiCo…AlgebraicGeometry.QuasiSeparated · cited by 52AlgebraicGeometry.QuasiSe…AlgebraicGeometry.Scheme.Hom.normalization · cited by 41Hom.normalizationAlgebraicGeometry.Scheme.Cover.RelativeGluingData.toBase · cited by 8RelativeGluingData.toBaseAlgebraicGeometry.Scheme.Hom.normalizationGlueData · cited by 3Hom.normalizationGlueDataHom.fromNormalizationCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by31

Results whose statement or proof uses this declaration.