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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.of_targetAffineLocally_of_isPullback

∀ {P : AlgebraicGeometry.AffineTargetMorphismProperty} [P.IsLocal] {X Y UX UY : AlgebraicGeometry.Scheme}
  [inst : AlgebraicGeometry.IsAffine UY] {f : X ⟶ Y} {iY : UY ⟶ Y} [AlgebraicGeometry.IsOpenImmersion iY] {iX : UX ⟶ X}
  {f' : UX ⟶ UY}, CategoryTheory.IsPullback iX f' f iY → AlgebraicGeometry.targetAffineLocally P f → P f'
Defined in
Mathlib.AlgebraicGeometry.Morphisms.Basic
Cited by
2 results in Mathlib
Foundations
Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.AffineTargetMorphismProperty.IsLocalAlgebraicGeometry.IsAffineAlgebraicGeometry.IsOpenImmersion
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Around this declaration

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AlgebraicGeometry.HasAffineProperty.of_isPullback · cited by 3HasAffineProperty.of_isPu…AlgebraicGeometry.HasAffineProperty.of_isZariskiLocalAtTarget · cited by 1HasAffineProperty.of_isZa…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.Iso.inv · cited by 6514Iso.invAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.Limits.pullback · cited by 864Limits.pullbackAlgebraicGeometry.IsOpenImmersion · cited by 476AlgebraicGeometry.IsOpenI…CategoryTheory.IsPullback · cited by 320CategoryTheory.IsPullbackAlgebraicGeometry.IsAffine · cited by 159AlgebraicGeometry.IsAffineAlgebraicGeometry.Scheme.Hom.opensRange · cited by 113Hom.opensRangeCategoryTheory.IsPullback.isoPullback · cited by 42IsPullback.isoPullbackAlgebraicGeometry.AffineTargetMorphismProperty · cited by 31AlgebraicGeometry.AffineT…AlgebraicGeometry.AffineTargetMorphismProperty.IsLocal · cited by 17AffineTargetMorphismPrope…AlgebraicGeometry.isAffineOpen_opensRange · cited by 13AlgebraicGeometry.isAffin…AlgebraicGeometry.targetAffineLocally · cited by 12AlgebraicGeometry.targetA…CategoryTheory.IsPullback.isoPullback_inv_snd · cited by 8IsPullback.isoPullback_in…AlgebraicGeometry.AffineTargetMorphismProperty.cancel_left_of_respectsIso · cited by 8AffineTargetMorphismPrope…AlgebraicGeometry.of_targetAf…CITED BYCITES

Cites17

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Cited by2

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