Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Flat.epi_of_flat_of_surjective
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.Flat f] [AlgebraicGeometry.Surjective f],
CategoryTheory.Epi fA flat surjective morphism of schemes is an epimorphism in the category of schemes.
- Defined in
- Mathlib.AlgebraicGeometry.Morphisms.Flat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objproof · cited by 19,642
- Algebraproof · cited by 11,388
- CategoryTheory.Functor.mapproof · cited by 8,698
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TopCat.carrierproof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- AlgebraicGeometry.PresheafedSpace.carrierproof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpaceproof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpaceproof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpaceproof · cited by 1,734
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isRegularEpi_of_flat_of_surjective_of_isAffineproof · cited by 0