Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isDominant_of_of_appTop_injective
∀ {X Y : AlgebraicGeometry.Scheme} [AlgebraicGeometry.IsAffine Y] {f : X ⟶ Y} [CompactSpace ↥X],
Function.Injective ⇑(CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.Scheme.Hom.appTop f)) →
AlgebraicGeometry.IsDominant fIf f : X ⟶ Y is a morphism of schemes with quasi-compact source and affine target,
f induces an injection on global sections, then f is dominant.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- RingHomstatement · cited by 10,189
- Top.topstatement and proof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Oppositestatement · cited by 8,081
- Bot.botproof · cited by 4,720
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- Set.univproof · cited by 3,945
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.