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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.isSeparated_iff_isClosedImmersion_prod_lift

∀ {X : AlgebraicGeometry.Scheme},
  X.IsSeparated ↔
    AlgebraicGeometry.IsClosedImmersion
      (CategoryTheory.Limits.prod.lift (CategoryTheory.CategoryStruct.id X) (CategoryTheory.CategoryStruct.id X))
Defined in
Mathlib.AlgebraicGeometry.Morphisms.Separated
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Foundations
Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
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Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Iso.hom · cited by 7684Iso.homCategoryTheory.Category.assoc · cited by 6433Category.assocCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteCategoryTheory.Limits.WalkingPair · cited by 1319Limits.WalkingPairCategoryTheory.Limits.pullback.fst · cited by 639pullback.fstCategoryTheory.Limits.pullback.snd · cited by 637pullback.sndCategoryTheory.Limits.pair · cited by 536Limits.pairCategoryTheory.Limits.prod · cited by 364Limits.prodCategoryTheory.Limits.limit.lift_π · cited by 266limit.lift_πCategoryTheory.Limits.prod.lift · cited by 123prod.liftCategoryTheory.Limits.BinaryFan.mk · cited by 112BinaryFan.mkScheme.isSeparated_iff_isClos…CITED BYCITES

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