Theorems · Inductive type · algebraic geometry
AlgebraicGeometry.Scheme.IsJointlySurjectivePreserving
CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme → Prop
A morphism property of schemes is said to preserve joint surjectivity, if
for any pair of morphisms f : X ⟶ S and g : Y ⟶ S where g satisfies P,
any pair of points x : X and y : Y with f x = g y can be lifted to a point
of X ×[S] Y.
In later files, this will be automatic, since this holds for any morphism g
(see AlgebraicGeometry.Scheme.isJointlySurjectivePreserving). But at
this early stage in the import tree, we only know it for open immersions.
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AlgebraicGeometry.Schemestatement · cited by 2,540
- CategoryTheory.MorphismPropertystatement · cited by 2,179
Cited by31
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Cover.pullbackHomstatement and proof · cited by 32
- AlgebraicGeometry.Scheme.Cover.Overstatement · cited by 23
- AlgebraicGeometry.Scheme.Cover.pullbackHom_mapstatement and proof · cited by 5
- AlgebraicGeometry.Scheme.Cover.pullbackCoverOverstatement and proof · cited by 3
- AlgebraicGeometry.Scheme.Cover.pullbackCoverOver'statement and proof · cited by 3
- AlgebraicGeometry.Scheme.Cover.pullbackCoverOverPropstatement and proof · cited by 3
- AlgebraicGeometry.Scheme.Cover.pullbackCoverOverProp'statement and proof · cited by 3
- AlgebraicGeometry.Scheme.Cover.pullbackHom_map_assocstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.IsJointlySurjectivePreserving.exists_preimage_fst_triplet_of_propstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.Cover.pullbackCoverOver_I₀statement and proof · cited by 0
- AlgebraicGeometry.Scheme.Cover.Over.mk.noConfusionstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.IsJointlySurjectivePreserving.casesOnstatement and proof · cited by 0