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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.IsAffine.of_isPullback

∀ {X Y Z P : AlgebraicGeometry.Scheme} {fst : P ⟶ X} {snd : P ⟶ Y} {f : X ⟶ Z} {g : Y ⟶ Z}
  [AlgebraicGeometry.IsAffine X] [AlgebraicGeometry.IsAffineHom g],
  CategoryTheory.IsPullback fst snd f g → AlgebraicGeometry.IsAffine P
Defined in
Mathlib.AlgebraicGeometry.Morphisms.Affine
Cited by
1 results in Mathlib
Foundations
Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.IsAffineAlgebraicGeometry.IsAffineHom
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Around this declaration

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

AlgebraicGeometry.isPushout_appTop_of_isPullback · cited by 0AlgebraicGeometry.isPusho…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.Iso.hom · cited by 7684Iso.homAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.IsPullback · cited by 320CategoryTheory.IsPullbackAlgebraicGeometry.IsAffine · cited by 159AlgebraicGeometry.IsAffineAlgebraicGeometry.IsAffineHom · cited by 63AlgebraicGeometry.IsAffin…CategoryTheory.IsPullback.isoPullback · cited by 42IsPullback.isoPullbackAlgebraicGeometry.IsAffine.of_isIso · cited by 11IsAffine.of_isIsoIsAffine.of_isPullbackCITED BYCITES

Cites8

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Cited by1

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