Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsClosedImmersion.of_comp_isClosedImmersion
∀ {X Y Z : AlgebraicGeometry.Scheme} (f : X ⟶ Y) (g : Y ⟶ Z) [AlgebraicGeometry.IsClosedImmersion g]
[AlgebraicGeometry.IsClosedImmersion (CategoryTheory.CategoryStruct.comp f g)], AlgebraicGeometry.IsClosedImmersion fIf f ≫ g and g are closed immersions, then f is a closed immersion.
Also see IsClosedImmersion.of_comp for the general version
where g is only required to be separated.
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- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
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