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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.IsSeparated.of_comp

∀ {X Y Z : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (g : Y ⟶ Z)
  [AlgebraicGeometry.IsSeparated (CategoryTheory.CategoryStruct.comp f g)], AlgebraicGeometry.IsSeparated f
Defined in
Mathlib.AlgebraicGeometry.Morphisms.Separated
Cited by
1 results in Mathlib
Foundations
Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AlgebraicGeometry.IsSeparated
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Around this declaration

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

AlgebraicGeometry.IsSeparated.comp_iff · cited by 0IsSeparated.comp_iffQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.Iso.inv · cited by 6514Iso.invCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.Category.comp_id · cited by 2119Category.comp_idCategoryTheory.Limits.pullback.snd · cited by 637pullback.sndCategoryTheory.Limits.pullback.map · cited by 156pullback.mapCategoryTheory.Limits.pullback.diagonal · cited by 67pullback.diagonalAlgebraicGeometry.IsClosedImmersion · cited by 49AlgebraicGeometry.IsClose…AlgebraicGeometry.IsSeparated · cited by 31AlgebraicGeometry.IsSepar…CategoryTheory.Limits.pullbackDiagonalMapIdIso · cited by 16Limits.pullbackDiagonalMa…AlgebraicGeometry.IsClosedImmersion.of_comp · cited by 3IsClosedImmersion.of_compIsSeparated.of_compCITED BYCITES

Cites13

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Cited by1

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