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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.surjective

∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.Surjective f], Function.Surjective ⇑f
Defined in
Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap
Cited by
12 results in Mathlib
Foundations
Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.Surjective

Around this declaration

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

AlgebraicGeometry.range_eq_univ · cited by 4AlgebraicGeometry.range_e…AlgebraicGeometry.isCommMonObj_of_isProper_of_isIntegral_tensorObj_of_isAlgClosed · cited by 1AlgebraicGeometry.isCommM…AlgebraicGeometry.Scheme.Hom.isConnected_preimage · cited by 1Hom.isConnected_preimageAlgebraicGeometry.exists_finite_imageι_comp_morphismRestrict_of_finite_image_preimage · cited by 1AlgebraicGeometry.exists_…AlgebraicGeometry.Scheme.Hom.isIrreducible_preimage · cited by 1Hom.isIrreducible_preimageAlgebraicGeometry.Flat.isQuotientMap_of_surjective · cited by 1Flat.isQuotientMap_of_sur…AlgebraicGeometry.Surjective.of_comp · cited by 1Surjective.of_compAlgebraicGeometry.isSheaf_fpqcTopology_continuousMapPresheaf · cited by 1AlgebraicGeometry.isSheaf…AlgebraicGeometry.HasRingHomProperty.descendsAlong_flat · cited by 0HasRingHomProperty.descen…AlgebraicGeometry.Scheme.Hom.one_le_finrank_iff_surjective · cited by 0Hom.one_le_finrank_iff_su…AlgebraicGeometry.IsOpenImmersion.of_flat_of_mono · cited by 0IsOpenImmersion.of_flat_o…AlgebraicGeometry.FormallyUnramified.hom_ext · cited by 0FormallyUnramified.hom_extDFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.ConcreteCategory.hom · cited by 4022ConcreteCategory.homTopCat.carrier · cited by 3184TopCat.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeContinuousMap · cited by 2491ContinuousMapCommRingCat · cited by 2333CommRingCatAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…TopCat · cited by 1889TopCatAlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…AlgebraicGeometry.PresheafedSpace.Hom.base · cited by 1135Hom.baseAlgebraicGeometry.LocallyRingedSpace.Hom.toHom · cited by 995Hom.toHomAlgebraicGeometry.Scheme.Hom.toLRSHom' · cited by 895Hom.toLRSHom'Hom.surjectiveCITED BYCITES

Cites17

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

Cited by12

Results whose statement or proof uses this declaration.