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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.normalizationDesc_comp

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [inst : AlgebraicGeometry.QuasiCompact f]
  [inst_1 : AlgebraicGeometry.QuasiSeparated f] {T : AlgebraicGeometry.Scheme} (f₁ : X ⟶ T) (f₂ : T ⟶ Y)
  [inst_2 : AlgebraicGeometry.IsIntegralHom f₂] (H : f = CategoryTheory.CategoryStruct.comp f₁ f₂),
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Hom.normalizationDesc f f₁ f₂ H) f₂ =
    AlgebraicGeometry.Scheme.Hom.fromNormalization f
Defined in
Mathlib.AlgebraicGeometry.Normalization
Cited by
5 results in Mathlib
Foundations
Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.QuasiCompactAlgebraicGeometry.QuasiSeparatedAlgebraicGeometry.IsIntegralHom

Around this declaration

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

AlgebraicGeometry.Scheme.Hom.normalizationPullback_snd · cited by 2Hom.normalizationPullback…AlgebraicGeometry.Scheme.Hom.inr_normalizationCoprodIso_hom_fromNormalization · cited by 1Hom.inr_normalizationCopr…AlgebraicGeometry.Scheme.Hom.normalizationCoprodIso_inv_coprodDesc_fromNormalization · cited by 1Hom.normalizationCoprodIs…AlgebraicGeometry.Scheme.Hom.inl_normalizationCoprodIso_hom_fromNormalization · cited by 1Hom.inl_normalizationCopr…AlgebraicGeometry.Scheme.Hom.normalizationDesc_comp_assoc · cited by 0Hom.normalizationDesc_com…DFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Functor.map · cited by 8698Functor.mapCategoryTheory.NatTrans.app · cited by 7406NatTrans.appCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.Category.assoc · cited by 6433Category.assocCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homLE.le.trans · cited by 3151le.transAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…AlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…Hom.normalizationDesc_compCITED BYCITES

Cites70

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Cited by5

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