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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.toNormalization_normalizationPullback_fst

∀ {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.toNormalization (CategoryTheory.Limits.pullback.snd f g))
      (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Hom.normalizationPullback f g)
        (CategoryTheory.Limits.pullback.fst (AlgebraicGeometry.Scheme.Hom.fromNormalization f) g)) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.fst f g)
      (AlgebraicGeometry.Scheme.Hom.toNormalization f)
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.QuasiCompactAlgebraicGeometry.QuasiSeparated
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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AlgebraicGeometry.Scheme.Hom.exists_mem_and_isIso_morphismRestrict_toNormalization · cited by 1Hom.exists_mem_and_isIso_…AlgebraicGeometry.Scheme.Hom.toNormalization_normalizationPullback_fst_assoc · cited by 0Hom.toNormalization_norma…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.Limits.pullback · cited by 864Limits.pullbackCategoryTheory.Limits.pullback.fst · cited by 639pullback.fstCategoryTheory.Limits.pullback.snd · cited by 637pullback.sndCategoryTheory.Limits.limit.lift_π · cited by 266limit.lift_πCategoryTheory.Limits.PullbackCone.mk · cited by 203PullbackCone.mkCategoryTheory.Limits.WalkingCospan.left · cited by 190WalkingCospan.leftCategoryTheory.Limits.pullback.map · cited by 156pullback.mapCategoryTheory.Limits.PullbackCone.mk_π_app · cited by 120PullbackCone.mk_π_appAlgebraicGeometry.QuasiCompact · cited by 102AlgebraicGeometry.QuasiCo…AlgebraicGeometry.QuasiSeparated · cited by 52AlgebraicGeometry.QuasiSe…AlgebraicGeometry.Scheme.Hom.normalization · cited by 41Hom.normalizationHom.toNormalization_normaliza…CITED BYCITES

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