Theorems · Definition · algebraic geometry
AlgebraicGeometry.ValuativeCriterion.Existence
CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme
A morphism f : X ⟶ Y satisfies the existence part of the valuative criterion if
every valuative commutative square over f has (at least) a lift.
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homproof · cited by 32,603
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.MorphismPropertystatement · cited by 2,179
- CategoryTheory.CommSq.HasLiftproof · cited by 20
- AlgebraicGeometry.ValuativeCommSqproof · cited by 9
- AlgebraicGeometry.ValuativeCommSq.commSqproof · cited by 4
Cited by11
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.ValuativeCriterion.iffstatement · cited by 3
- AlgebraicGeometry.UniversallyClosed.eq_valuativeCriterionstatement and proof · cited by 2
- AlgebraicGeometry.IsSeparated.of_valuativeCriterionproof · cited by 1
- AlgebraicGeometry.ValuativeCriterion.eqstatement and proof · cited by 1
- AlgebraicGeometry.IsProper.eq_valuativeCriterionproof · cited by 1
- AlgebraicGeometry.ValuativeCriterion.Existence.eqstatement and proof · cited by 1
- AlgebraicGeometry.ValuativeCriterion.Existence.of_specializingMapstatement · cited by 1
- AlgebraicGeometry.ValuativeCriterion.Existence.specializingMapstatement and proof · cited by 1
- AlgebraicGeometry.UniversallyClosed.of_valuativeCriterionstatement and proof · cited by 1
- AlgebraicGeometry.ValuativeCriterion.existencestatement · cited by 0
- AlgebraicGeometry.Proj.valuativeCriterion_existencestatement · cited by 0