Theorems · Theorem · algebraic geometry

AlgebraicGeometry.injective_germ_basicOpen

∀ {X : AlgebraicGeometry.Scheme} (U : X.Opens),
  AlgebraicGeometry.IsAffineOpen U →
    ∀ (x : ↥X) (hx : x ∈ U) (f : ↑(X.presheaf.obj (Opposite.op U))) (hf : x ∈ X.basicOpen f),
      Function.Injective ⇑(CategoryTheory.ConcreteCategory.hom (X.presheaf.germ U x hx)) →
        Function.Injective ⇑(CategoryTheory.ConcreteCategory.hom (X.presheaf.germ (X.basicOpen f) x hf))

Defined in: Mathlib.AlgebraicGeometry.SpreadingOut
Cited by: 1 results in Mathlib
Foundations: Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound

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Cites40

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 and proof · cited by 19,642
RingHomstatement and proof · cited by 10,189
CategoryTheory.Functor.mapproof · cited by 8,698
Oppositestatement · cited by 8,081
CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
TopCat.carrierstatement and proof · 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 and proof · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988

Cited by1

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.exists_le_and_germ_injectiveproof · cited by 3