Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Flat.isQuotientMap_of_surjective
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.Flat f] [AlgebraicGeometry.QuasiCompact f]
[AlgebraicGeometry.Surjective f], Topology.IsQuotientMap ⇑fA surjective, quasi-compact, flat morphism is a quotient map.
- Defined in
- Mathlib.AlgebraicGeometry.Morphisms.Flat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites68
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Top.topproof · cited by 9,680
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- CategoryTheory.Category.assocproof · cited by 6,433
- Set.preimageproof · 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
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isSheaf_fpqcTopology_continuousMapPresheafproof · cited by 1