Mathlib Map

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
Defined in
Mathlib.AlgebraicGeometry.Morphisms.FlatRank
Cited by
7 results in Mathlib
Foundations
Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.IsIsoAlgebraicGeometry.FlatAlgebraicGeometry.IsFinite

Around this declaration

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

AlgebraicGeometry.Scheme.Hom.finrank_pullback_snd · cited by 6Hom.finrank_pullback_sndAlgebraicGeometry.Scheme.Hom.one_le_finrank_map · cited by 1Hom.one_le_finrank_mapAlgebraicGeometry.Scheme.Hom.finrank_eq_one_of_isIso · cited by 1Hom.finrank_eq_one_of_isI…AlgebraicGeometry.Scheme.Hom.finrank_of_isPullback · cited by 1Hom.finrank_of_isPullbackAlgebraicGeometry.Scheme.Hom.one_le_finrank_iff_surjective · cited by 0Hom.one_le_finrank_iff_su…AlgebraicGeometry.Scheme.Hom.isIso_iff_finrank_eq · cited by 0Hom.isIso_iff_finrank_eqAlgebraicGeometry.Scheme.Hom.isLocallyConstant_finrank · cited by 0Hom.isLocallyConstant_fin…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.Category.assoc · cited by 6433Category.assocCategoryTheory.Iso · cited by 3963CategoryTheory.IsoTopCat.carrier · cited by 3184TopCat.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…AlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…CategoryTheory.IsIso · cited by 1156CategoryTheory.IsIsoCategoryTheory.Iso.symm · cited by 993Iso.symmHom.finrank_comp_left_of_isIsoCITED BYCITES

Cites30

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

Cited by7

Results whose statement or proof uses this declaration.