Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.normalizationPullback_snd

∀ {X S Y : AlgebraicGeometry.Scheme} (f : X ⟶ S) (g : Y ⟶ S) [inst : AlgebraicGeometry.QuasiCompact f]
  [inst_1 : AlgebraicGeometry.QuasiSeparated f],
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Hom.normalizationPullback f g)
      (CategoryTheory.Limits.pullback.snd (AlgebraicGeometry.Scheme.Hom.fromNormalization f) g) =
    AlgebraicGeometry.Scheme.Hom.fromNormalization (CategoryTheory.Limits.pullback.snd f g)

Defined in: Mathlib.AlgebraicGeometry.Normalization
Cited by: 2 results in Mathlib
Foundations: Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AlgebraicGeometry.QuasiCompact AlgebraicGeometry.QuasiSeparated

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Cites14

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

Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.CategoryStruct.idproof · cited by 6,235
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CategoryTheory.Limits.pullbackstatement · cited by 864
CategoryTheory.Limits.pullback.sndstatement and proof · cited by 637
CategoryTheory.Limits.pullback.mapproof · cited by 156
AlgebraicGeometry.QuasiCompactstatement and proof · cited by 102
AlgebraicGeometry.QuasiSeparatedstatement and proof · cited by 52
AlgebraicGeometry.Scheme.Hom.normalizationstatement · cited by 41
AlgebraicGeometry.Scheme.Hom.fromNormalizationstatement and proof · cited by 28
AlgebraicGeometry.Scheme.Hom.toNormalizationproof · cited by 28

Cited by2

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.Hom.exists_mem_and_isIso_morphismRestrict_toNormalizationproof · cited by 1
AlgebraicGeometry.Scheme.Hom.normalizationPullback_snd_assocproof · cited by 0