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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.IsSeparated.isClosedImmersion_diagonal

∀ {X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y} [self : AlgebraicGeometry.IsSeparated f],
  AlgebraicGeometry.IsClosedImmersion (CategoryTheory.Limits.pullback.diagonal f)

A morphism is separated if the diagonal map is a closed immersion.

Defined in
Mathlib.AlgebraicGeometry.Morphisms.Separated
Cited by
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Foundations
Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.IsSeparated
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Quiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.Limits.pullback.diagonalObj · cited by 80pullback.diagonalObjCategoryTheory.Limits.pullback.diagonal · cited by 67pullback.diagonalAlgebraicGeometry.IsClosedImmersion · cited by 49AlgebraicGeometry.IsClose…AlgebraicGeometry.IsSeparated · cited by 31AlgebraicGeometry.IsSepar…IsSeparated.isClosedImmersion…CITED BYCITES

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