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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.UniversallyClosed.of_comp_of_isSeparated

∀ {X Y Z : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (g : Y ⟶ Z)
  [AlgebraicGeometry.UniversallyClosed (CategoryTheory.CategoryStruct.comp f g)] [AlgebraicGeometry.IsSeparated g],
  AlgebraicGeometry.UniversallyClosed f

[Stacks Tag 01W6](https://stacks.math.columbia.edu/tag/01W6) ((1))

Defined in
Mathlib.AlgebraicGeometry.Morphisms.Proper
Cited by
1 results in Mathlib
Foundations
Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.UniversallyClosedAlgebraicGeometry.IsSeparated
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Around this declaration

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

AlgebraicGeometry.isIntegral_appTop_of_universallyClosed · cited by 1AlgebraicGeometry.isInteg…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.IsSeparated · cited by 31AlgebraicGeometry.IsSepar…AlgebraicGeometry.UniversallyClosed · cited by 24AlgebraicGeometry.Univers…CategoryTheory.MorphismProperty.of_postcomp · cited by 17MorphismProperty.of_postc…UniversallyClosed.of_comp_of_…CITED BYCITES

Cites6

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Cited by1

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