Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.finiteType_appLE
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [self : AlgebraicGeometry.LocallyOfFiniteType f] {U : Y.Opens},
AlgebraicGeometry.IsAffineOpen U →
∀ {V : X.Opens},
AlgebraicGeometry.IsAffineOpen V →
∀ (e : V ≤ (TopologicalSpace.Opens.map f.base).obj U),
(CommRingCat.Hom.hom (AlgebraicGeometry.Scheme.Hom.appLE f U V e)).FiniteTypeAlias of AlgebraicGeometry.LocallyOfFiniteType.finiteType_appLE.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- Oppositestatement · cited by 8,081
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement · cited by 2,540
- 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
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
- AlgebraicGeometry.Scheme.Opensstatement · cited by 1,149
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.exists_etale_isCompl_of_quasiFiniteAtproof · cited by 1
- AlgebraicGeometry.spread_out_of_isGermInjectiveproof · cited by 1
- AlgebraicGeometry.LocallyOfFiniteType.finiteType_of_affine_subsetproof · cited by 0
- AlgebraicGeometry.essentiallySmall_costructuredArrow_Specproof · cited by 0
- AlgebraicGeometry.finite_appTop_of_universallyClosedproof · cited by 0