Mathlib Map

Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.Hom.normalizationDiagram

{X Y : AlgebraicGeometry.Scheme} → (X ⟶ Y) → CategoryTheory.Functor Y.Opensᵒᵖ CommRingCat

Given a morphism f : X ⟶ Y, this is the presheaf of integral closure of Y in X.

Defined in
Mathlib.AlgebraicGeometry.Normalization
Cited by
8 results in Mathlib
Foundations
Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

AlgebraicGeometry.Scheme.Hom.normalizationDiagramMap · cited by 8Hom.normalizationDiagramM…AlgebraicGeometry.Scheme.Hom.normalizationObjIso · cited by 6Hom.normalizationObjIsoAlgebraicGeometry.Scheme.Hom.normalizationDesc_comp · cited by 5Hom.normalizationDesc_compAlgebraicGeometry.Scheme.Hom.ι_fromNormalization · cited by 4Hom.ι_fromNormalizationAlgebraicGeometry.Scheme.Hom.toNormalization_app_preimage · cited by 2Hom.toNormalization_app_p…AlgebraicGeometry.Scheme.Hom.coequifibered_normalizationDiagramMap · cited by 1Hom.coequifibered_normali…AlgebraicGeometry.Scheme.Hom.fromNormalization_app · cited by 1Hom.fromNormalization_appAlgebraicGeometry.Scheme.Hom.ι_fromNormalization_assoc · cited by 0Hom.ι_fromNormalization_a…AlgebraicGeometry.Scheme.Hom.preservesLocalization_normalizationDiagramMap · cited by 0Hom.preservesLocalization…AlgebraicGeometry.Scheme.Hom.normalization.hom_ext · cited by 0normalization.hom_extQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.Functor · cited by 16252CategoryTheory.FunctorCategoryTheory.Functor.map · cited by 8698Functor.mapOpposite · cited by 8081OppositeTopCat.carrier · cited by 3184TopCat.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatOpposite.unop · cited by 2231Opposite.unopAlgebraicGeometry.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…AlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…AlgebraicGeometry.Scheme.Opens · cited by 1149Scheme.OpensHom.normalizationDiagramCITED BYCITES

Cites26

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

Cited by10

Results whose statement or proof uses this declaration.