Theorems · Theorem · algebraic geometry

AlgebraicGeometry.IsAffineOpen.basicOpen_basicOpen_is_basicOpen

∀ {X : AlgebraicGeometry.Scheme} {U : X.Opens},
  AlgebraicGeometry.IsAffineOpen U →
    ∀ (f : ↑(X.presheaf.obj (Opposite.op U))) (g : ↑(X.presheaf.obj (Opposite.op (X.basicOpen f)))),
      ∃ f', X.basicOpen f' = X.basicOpen g

Defined in: Mathlib.AlgebraicGeometry.AffineScheme
Cited by: 2 results in Mathlib
Foundations: Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites39

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

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Oppositestatement · cited by 8,081
Algebra.algebraMapproof · cited by 4,706
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TopologicalSpace.Opensstatement · cited by 2,040
AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988

Cited by2

Results whose statement or proof uses this declaration.

AlgebraicGeometry.exists_basicOpen_le_affine_interproof · cited by 7
AlgebraicGeometry.Scheme.AffineZariskiSite.generate_presieveOfSectionsproof · cited by 0