Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.fromSpecStalk_app

∀ {X : AlgebraicGeometry.Scheme} {U : X.Opens} {x : ↥X} (hxU : x ∈ U),
  AlgebraicGeometry.Scheme.Hom.app (X.fromSpecStalk x) U =
    CategoryTheory.CategoryStruct.comp (X.presheaf.germ U x hxU)
      (CategoryTheory.CategoryStruct.comp (AlgebraicGeometry.Scheme.ΓSpecIso (X.presheaf.stalk x)).inv
        ((AlgebraicGeometry.Spec (X.presheaf.stalk x)).presheaf.map (CategoryTheory.homOfLE ⋯).op))

Defined in: Mathlib.AlgebraicGeometry.Stalk
Cited by: 2 results in Mathlib
Foundations: Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites52

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
CategoryTheory.Iso.invstatement and proof · cited by 6,514
CategoryTheory.Category.assocproof · cited by 6,433
Set.imageproof · cited by 5,609

Cited by2

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.germ_stalkClosedPointTo_Spec_fromSpecStalkproof · cited by 2
AlgebraicGeometry.Scheme.fromSpecStalk_appTopproof · cited by 1