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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.Hom.isClosedMap

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

Around this declaration

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

AlgebraicGeometry.universallyClosed_eq_universallySpecializing · cited by 1AlgebraicGeometry.univers…AlgebraicGeometry.isCommMonObj_of_isProper_of_isIntegral_tensorObj_of_isAlgClosed · cited by 1AlgebraicGeometry.isCommM…AlgebraicGeometry.IsSeparated.of_valuativeCriterion · cited by 1IsSeparated.of_valuativeC…AlgebraicGeometry.Scheme.Hom.closePoints_subset_preimage_closedPoints · cited by 1Hom.closePoints_subset_pr…AlgebraicGeometry.exists_etale_isCompl_of_quasiFiniteAt · cited by 1AlgebraicGeometry.exists_…AlgebraicGeometry.Scheme.Hom.isProperMap · cited by 0Hom.isProperMapDFunLike.coe · cited by 62936DFunLike.coeQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.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.toHomHom.isClosedMapCITED BYCITES

Cites20

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

Cited by6

Results whose statement or proof uses this declaration.