Theorems · Theorem · algebraic geometry

AlgebraicGeometry.IsAffineOpen.fromSpec_app_self

∀ {X : AlgebraicGeometry.Scheme} {U : X.Opens} (hU : AlgebraicGeometry.IsAffineOpen U),
  AlgebraicGeometry.Scheme.Hom.app hU.fromSpec U =
    CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.ΓSpecIso (X.presheaf.obj (Opposite.op U))).inv
      ((AlgebraicGeometry.Spec (X.presheaf.obj (Opposite.op U))).presheaf.map (CategoryTheory.eqToHom ⋯).op)

Defined in: Mathlib.AlgebraicGeometry.AffineScheme
Cited by: 6 results in Mathlib
Foundations: Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound

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

Cites31

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

Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
Top.topstatement and proof · cited by 9,680
CategoryTheory.Functor.mapstatement · cited by 8,698
Oppositestatement · cited by 8,081
CategoryTheory.Iso.invstatement and proof · cited by 6,514
TopCat.carrierstatement · cited by 3,184
AlgebraicGeometry.Schemestatement and proof · cited by 2,540
CommRingCatstatement · cited by 2,333
TopologicalSpace.Opensstatement · cited by 2,040
AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020

Cited by6

Results whose statement or proof uses this declaration.

AlgebraicGeometry.IsAffineOpen.isLocalization_basicOpenproof · cited by 18
AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_appproof · cited by 5
AlgebraicGeometry.IsAffineOpen.isLocalization_stalk'proof · cited by 2
AlgebraicGeometry.Scheme.Hom.fromNormalization_appproof · cited by 1
AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpen'proof · cited by 1
AlgebraicGeometry.IsAffineOpen.fromSpec_app_self_applyproof · cited by 0