Theorems · Theorem · algebraic geometry

AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq

∀ {A : Type u_1} {σ : Type u_2} [inst : CommRing A] [inst_1 : SetLike σ A] [inst_2 : AddSubgroupClass σ A] (𝒜 : ℕ → σ)
  [inst_3 : GradedRing 𝒜] {f : A} (x : ↑((AlgebraicGeometry.Proj.toLocallyRingedSpace 𝒜).restrict ⋯).toTopCat),
  (CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec 𝒜 f).base) x =
    (CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec 𝒜 f)) x

Defined in: Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme
Cited by: 3 results in Mathlib
Foundations: Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing SetLike AddSubgroupClass GradedRing

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Cites57

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 · cited by 19,642
CommRingstatement and proof · cited by 17,173
CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
TopCat.carrierstatement and proof · cited by 3,184
ContinuousMapstatement · cited by 2,491
CommRingCatstatement · cited by 2,333
TopologicalSpace.Opensstatement · cited by 2,040
AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
TopCatstatement · cited by 1,889

Cited by3

Results whose statement or proof uses this declaration.

AlgebraicGeometry.ProjectiveSpectrum.Proj.mk_mem_toSpec_base_applyproof · cited by 1
AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_isIsoproof · cited by 1
AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_preimage_basicOpenproof · cited by 0