Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.AffineZariskiSite.opensRange_relativeGluingData_map

∀ {X : AlgebraicGeometry.Scheme} (F : CategoryTheory.Functor X.AffineZariskiSiteᵒᵖ CommRingCat)
  (α : (AlgebraicGeometry.Scheme.AffineZariskiSite.toOpensFunctor X).op.comp X.presheaf ⟶ F)
  (H : CategoryTheory.NatTrans.Coequifibered α) {U : X.AffineZariskiSite} (r : ↑(X.presheaf.obj (Opposite.op ↑U))),
  AlgebraicGeometry.Scheme.Hom.opensRange
      ((AlgebraicGeometry.Scheme.AffineZariskiSite.relativeGluingData H).functor.map (CategoryTheory.homOfLE ⋯)) =
    PrimeSpectrum.basicOpen ((CategoryTheory.ConcreteCategory.hom (α.app (Opposite.op U))) r)

Defined in: Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski
Cited by: 1 results in Mathlib
Foundations: Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound

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CategoryTheory.Functor.compstatement and proof · cited by 6,529
CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
TopCat.carrierstatement · cited by 3,184

Cited by1

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AlgebraicGeometry.Scheme.AffineZariskiSite.PreservesLocalization.opensRange_mapproof · cited by 0