Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Spec.fromSpecStalk_eq

∀ (R : CommRingCat) (x : ↥(AlgebraicGeometry.Spec R)),
  (AlgebraicGeometry.Spec R).fromSpecStalk x =
    AlgebraicGeometry.Spec.map
      (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.ΓSpecIso R).inv
        ((AlgebraicGeometry.Spec R).presheaf.germ ⊤ x trivial))

Defined in: Mathlib.AlgebraicGeometry.Stalk
Cited by: 4 results in Mathlib
Foundations: Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites27

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
Oppositestatement · cited by 8,081
CategoryTheory.Iso.invstatement and proof · cited by 6,514
TopCat.carrierstatement and proof · cited by 3,184
AlgebraicGeometry.Schemestatement · cited by 2,540
CommRingCatstatement and proof · cited by 2,333
TopologicalSpace.Opensstatement · cited by 2,040
AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988

Cited by4

Results whose statement or proof uses this declaration.

AlgebraicGeometry.LocallyQuasiFinite.of_fiberToSpecResidueFieldproof · cited by 2
AlgebraicGeometry.Spec.fromSpecStalk_eq'proof · cited by 2
AlgebraicGeometry.Scheme.Spec.map_residueFieldIso_inv_eq_fromSpecResidueFieldproof · cited by 1
AlgebraicGeometry.Scheme.Spec_fromSpecStalkproof · cited by 0