Theorems · Theorem · algebraic geometry

AlgebraicGeometry.basicOpen_eq_of_affine

∀ {R : CommRingCat} (f : ↑R),
  (AlgebraicGeometry.Spec R).basicOpen
      ((CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.Scheme.ΓSpecIso R).inv) f) =
    PrimeSpectrum.basicOpen f

Defined in: Mathlib.AlgebraicGeometry.Scheme
Cited by: 5 results in Mathlib
Foundations: Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites34

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

DFunLike.coestatement and proof · cited by 62,936
CategoryTheory.Functor.objstatement · cited by 19,642
RingHomstatement · cited by 10,189
Top.topstatement · cited by 9,680
Oppositestatement · cited by 8,081
CategoryTheory.Iso.invstatement and proof · cited by 6,514
Algebra.algebraMapproof · cited by 4,706
CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
TopCat.carrierstatement and proof · cited by 3,184
CommRingCatstatement and proof · cited by 2,333
Set.extproof · cited by 2,266
TopologicalSpace.Opensstatement · cited by 2,040

Cited by5

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.toSpecΓ_preimage_basicOpenproof · cited by 7
AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpenproof · cited by 5
AlgebraicGeometry.IsAffineOpen.Spec_basicOpenproof · cited by 2
AlgebraicGeometry.basicOpen_eq_of_affine'proof · cited by 2
AlgebraicGeometry.Scheme.IsGermInjective.Specproof · cited by 0