Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsFinite.SpecMap_iff
∀ {R S : CommRingCat} (f : R ⟶ S),
AlgebraicGeometry.IsFinite (AlgebraicGeometry.Spec.map f) ↔ (CommRingCat.Hom.hom f).Finite- Cited by
- 1 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- CommRingCatstatement and proof · cited by 2,333
- CommRingCat.carrierstatement · cited by 1,096
- AlgebraicGeometry.Specstatement · cited by 626
- CommRingCat.Hom.homstatement and proof · cited by 432
- AlgebraicGeometry.Spec.mapstatement and proof · cited by 332
- AlgebraicGeometry.Scheme.Hom.appTopproof · cited by 109
- RingHom.Finitestatement and proof · cited by 48
- AlgebraicGeometry.IsFinitestatement · cited by 33
- AlgebraicGeometry.HasAffineProperty.iff_of_isAffineproof · cited by 21
- AlgebraicGeometry.arrowIsoΓSpecOfIsAffineproof · cited by 6
- RingHom.RespectsIso.arrow_mk_iso_iffproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isFinite_iff_locallyOfFiniteType_of_jacobsonSpaceproof · cited by 1