Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.IdealSheafData.subschemeMap
{X Y : AlgebraicGeometry.Scheme} →
(I : X.IdealSheafData) → (J : Y.IdealSheafData) → (f : X ⟶ Y) → J ≤ I.map f → (I.subscheme ⟶ J.subscheme)If J ≤ I.map f, then f restricts to a map I ⟶ J between the closed subschemes.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 220 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
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- AlgebraicGeometry.Scheme.IdealSheafDatastatement and proof · cited by 192
- AlgebraicGeometry.Scheme.IdealSheafData.subschemestatement · cited by 36
- AlgebraicGeometry.Scheme.IdealSheafData.subschemeιproof · cited by 36
- AlgebraicGeometry.Scheme.IdealSheafData.mapstatement and proof · cited by 19
- AlgebraicGeometry.IsClosedImmersion.liftproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.IdealSheafData.subschemeMap_subschemeιstatement · cited by 3
- AlgebraicGeometry.Scheme.IdealSheafData.comapIso_hom_sndstatement · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.subschemeMap_subschemeι_assocstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.subschemeMap.congr_simpstatement and proof · cited by 1
- AlgebraicGeometry.exists_mem_of_isClosed_of_nonemptyproof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.comapIso_hom_snd_assocstatement and proof · cited by 0