Documentation

Mathlib.AlgebraicGeometry.Over

Typeclasses for S-schemes and S-morphisms #

We define these as thin wrappers around CategoryTheory/Comma/OverClass.

Main definition #

@[reducible, inline]

X.Over S is the typeclass containing the data of a structure morphism X ↘ S : X ⟶ S.

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@[reducible, inline]

X.CanonicallyOver S is the typeclass containing the data of a structure morphism X ↘ S : X ⟶ S, and that S is (uniquely) inferable from the structure of X.

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@[reducible, inline]
abbrev AlgebraicGeometry.Scheme.Hom.IsOver {X Y : Scheme} (f : X.Hom Y) (S : Scheme) [X.Over S] [Y.Over S] :

Given X.Over S and Y.Over S and f : X ⟶ Y, f.IsOver S is the typeclass asserting f commutes with the structure morphisms.

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@[simp]

Also note the existence of CategoryTheory.IsOverTower X Y S.