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Theorems · Inductive type · algebraic geometry

AlgebraicGeometry.UniversallyOpen

{X Y : AlgebraicGeometry.Scheme} → (X ⟶ Y) → Prop

A morphism of schemes f : X ⟶ Y is universally open if the base change X ×[Y] Y' ⟶ Y' along any morphism Y' ⟶ Y is (topologically) an open map.

Defined in
Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen
Cited by
8 results in Mathlib
Foundations
Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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AlgebraicGeometry.Scheme.Hom.isOpenMap · cited by 5Hom.isOpenMapAlgebraicGeometry.UniversallyOpen.universally_isOpenMap · cited by 2UniversallyOpen.universal…AlgebraicGeometry.universallyOpen_iff · cited by 1AlgebraicGeometry.univers…AlgebraicGeometry.UniversallyOpen.casesOn · cited by 1UniversallyOpen.casesOnAlgebraicGeometry.GeometricallyIrreducible.comp · cited by 0GeometricallyIrreducible.…AlgebraicGeometry.GeometricallyConnected.comp · cited by 0GeometricallyConnected.co…AlgebraicGeometry.UniversallyOpen.out · cited by 0UniversallyOpen.outAlgebraicGeometry.UniversallyOpen.recOn · cited by 0UniversallyOpen.recOnAlgebraicGeometry.GeometricallyIntegral.isIntegral_of_isLocallyNoetherian · cited by 0GeometricallyIntegral.isI…AlgebraicGeometry.UniversallyOpen.eq · cited by 0UniversallyOpen.eqQuiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.Universally…CITED BYCITES

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Cited by10

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