Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.isIrreducible_preimage
∀ {X S : AlgebraicGeometry.Scheme} (f : X ⟶ S) [AlgebraicGeometry.GeometricallyIrreducible f],
IsOpenMap ⇑f → ∀ {s : Set ↥S}, IsIrreducible s → IsIrreducible (⇑f ⁻¹' s)- 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.
Cites36
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
- Setstatement and proof · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- Set.preimagestatement · cited by 4,946
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- Set.Nonemptyproof · cited by 2,627
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.GeometricallyIrreducible.irreducibleSpaceproof · cited by 2