Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.RationalMap.toRationalMap_comp
∀ {X Y Z : AlgebraicGeometry.Scheme} [inst : PreirreducibleSpace ↥X] [inst_1 : Nonempty ↥Y] (f : X.PartialMap Y)
[inst_2 : AlgebraicGeometry.IsDominant f.hom] (g : Y.PartialMap Z),
f.toRationalMap.comp g.toRationalMap = (f.comp g).toRationalMap- Cited by
- 1 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
- AlgebraicGeometry.Scheme.Opens.toSchemestatement · cited by 433
- AlgebraicGeometry.Scheme.PartialMapstatement and proof · cited by 76
- AlgebraicGeometry.Scheme.PartialMap.domainstatement · cited by 60
- AlgebraicGeometry.Scheme.PartialMap.homstatement and proof · cited by 49
- AlgebraicGeometry.IsDominantstatement and proof · cited by 43
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.RationalMap.id_compproof · cited by 0