Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Flat.isIso_of_surjective_of_mono
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.Flat f] [AlgebraicGeometry.QuasiCompact f]
[AlgebraicGeometry.Surjective f] [CategoryTheory.Mono f], CategoryTheory.IsIso f[Stacks Tag 06NC](https://stacks.math.columbia.edu/tag/06NC)
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.IsIsostatement · cited by 1,156
- CategoryTheory.Monostatement and proof · cited by 893
- AlgebraicGeometry.QuasiCompactstatement and proof · cited by 102
- AlgebraicGeometry.Flatstatement and proof · cited by 49
- AlgebraicGeometry.Surjectivestatement and proof · cited by 48
- CategoryTheory.MorphismProperty.of_pullback_fst_of_descendsAlongproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsOpenImmersion.of_flat_of_monoproof · cited by 0