Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.finrank_comp_left_of_isIso
∀ {X S Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (g : Y ⟶ S) [CategoryTheory.IsIso f] [AlgebraicGeometry.Flat g]
[AlgebraicGeometry.IsFinite g],
AlgebraicGeometry.Scheme.Hom.finrank (CategoryTheory.CategoryStruct.comp f g) = AlgebraicGeometry.Scheme.Hom.finrank g- Cited by
- 7 results in Mathlib
- Foundations
- Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Isoproof · cited by 3,963
- 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
Cited by7
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.finrank_pullback_sndproof · cited by 6
- 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