Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.normalizationCoprodIso_inv_coprodDesc_fromNormalization

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [inst : AlgebraicGeometry.QuasiCompact f]
  [inst_1 : AlgebraicGeometry.QuasiSeparated f] {U V : AlgebraicGeometry.Scheme} {iU : U ⟶ X} {iV : V ⟶ X}
  (e : CategoryTheory.Limits.IsColimit (CategoryTheory.Limits.BinaryCofan.mk iU iV))
  [inst_2 : AlgebraicGeometry.QuasiCompact iU] [inst_3 : AlgebraicGeometry.QuasiSeparated iU]
  [inst_4 : AlgebraicGeometry.QuasiCompact iV] [inst_5 : AlgebraicGeometry.QuasiSeparated iV],
  CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.Hom.normalizationCoprodIso f e).inv
      (CategoryTheory.Limits.coprod.desc
        (AlgebraicGeometry.Scheme.Hom.fromNormalization (CategoryTheory.CategoryStruct.comp iU f))
        (AlgebraicGeometry.Scheme.Hom.fromNormalization (CategoryTheory.CategoryStruct.comp iV f))) =
    AlgebraicGeometry.Scheme.Hom.fromNormalization f

Defined in

Mathlib.AlgebraicGeometry.Normalization

Cited by

1 results in Mathlib

Foundations

Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AlgebraicGeometry.QuasiCompactAlgebraicGeometry.QuasiSeparatedAlgebraicGeometry.QuasiCompactAlgebraicGeometry.QuasiSeparatedAlgebraicGeometry.QuasiCompactAlgebraicGeometry.QuasiSeparated