Theorems · Theorem · algebraic geometry
AlgebraicGeometry.LocallyQuasiFinite.of_finite_preimage_singleton
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.LocallyOfFiniteType f],
(∀ (x : ↥Y), (⇑f ⁻¹' {x}).Finite) → AlgebraicGeometry.LocallyQuasiFinite f- Cited by
- 2 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites47
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
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- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- Algebraproof · cited by 11,388
- Set.preimagestatement and proof · cited by 4,946
- 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
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement and proof · cited by 2,333
- Set.extproof · cited by 2,266
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.locallyQuasiFinite_iff_finite_preimage_singletonproof · cited by 0
- AlgebraicGeometry.LocallyQuasiFinite.of_injectiveproof · cited by 0