Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Hom.liftCoborder
{X Y : AlgebraicGeometry.Scheme} →
(f : X ⟶ Y) → [inst : AlgebraicGeometry.IsImmersion f] → X ⟶ ↑(AlgebraicGeometry.Scheme.Hom.coborderRange f)The first part of the factorization of an immersion f : X ⟶ Y to a closed immersion
f.liftCoborder : X ⟶ f.coborderRange and a dominant open immersion f.coborderRange.ι.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- AlgebraicGeometry.Scheme.Opens.toSchemestatement · cited by 433
- AlgebraicGeometry.Scheme.Opens.ιproof · cited by 275
- AlgebraicGeometry.IsOpenImmersion.liftproof · cited by 20
- AlgebraicGeometry.IsImmersionstatement and proof · cited by 17
- AlgebraicGeometry.Scheme.Hom.coborderRangestatement and proof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.liftCoborder_ιstatement · cited by 6
- AlgebraicGeometry.Scheme.Hom.liftCoborder_preimagestatement and proof · cited by 2
- AlgebraicGeometry.liftCoborder_appstatement and proof · cited by 1
- AlgebraicGeometry.IsImmersion.isPullback_toImage_liftCoborderstatement and proof · cited by 0
- AlgebraicGeometry.IsImmersion.isImmersion_iff_existsproof · cited by 0
- AlgebraicGeometry.Scheme.Hom.liftCoborder_ι_assocstatement and proof · cited by 0