Mathlib Map

Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.RationalMap.isOver_iff

∀ {X Y S : AlgebraicGeometry.Scheme} [inst : X.Over S] [inst_1 : Y.Over S] {f : X.RationalMap Y},
  AlgebraicGeometry.Scheme.RationalMap.IsOver S f ↔
    f.compHom (Y ↘ S) = AlgebraicGeometry.Scheme.Hom.toRationalMap (X ↘ S)
Defined in
Mathlib.AlgebraicGeometry.Birational.RationalMap
Cited by
0 results in Mathlib
Foundations
Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.Scheme.OverAlgebraicGeometry.Scheme.Over
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compTop.top · cited by 9680Top.topSetLike.coe · cited by 8199SetLike.coeCategoryTheory.Category.assoc · cited by 6433Category.assocAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.Scheme.Opens · cited by 1149Scheme.OpensAlgebraicGeometry.Scheme.Opens.toScheme · cited by 433Opens.toSchemeDense · cited by 359DenseAlgebraicGeometry.Scheme.Opens.ι · cited by 275Opens.ιAlgebraicGeometry.Scheme.homOfLE · cited by 103Scheme.homOfLEAlgebraicGeometry.Scheme.PartialMap · cited by 76Scheme.PartialMapCategoryTheory.over · cited by 76CategoryTheory.overCategoryTheory.OverClass · cited by 68CategoryTheory.OverClassAlgebraicGeometry.Scheme.PartialMap.domain · cited by 60PartialMap.domainAlgebraicGeometry.Scheme.PartialMap.hom · cited by 49PartialMap.homRationalMap.isOver_iffCITED BYCITES

Cites33

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.