Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.finrank_pullback_snd
∀ {X Y Z : AlgebraicGeometry.Scheme} (f : X ⟶ Z) (g : Y ⟶ Z) [AlgebraicGeometry.Flat f] [AlgebraicGeometry.IsFinite f]
(y : ↥Y),
AlgebraicGeometry.Scheme.Hom.finrank (CategoryTheory.Limits.pullback.snd f g) y =
AlgebraicGeometry.Scheme.Hom.finrank f (g y)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 223 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement and proof · 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
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.one_le_finrank_mapproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.finrank_eq_one_of_isIsoproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.finrank_of_isPullbackproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.one_le_finrank_iff_surjectiveproof · cited by 0
- AlgebraicGeometry.Scheme.Hom.isIso_iff_finrank_eqproof · cited by 0
- AlgebraicGeometry.Scheme.Hom.isLocallyConstant_finrankproof · cited by 0