subschemeFunctor — Mathlib

English

A continuation of functorial behavior in the opposite category.

Русский

Продолжение поведения функторa в противоположной категории.

LaTeX

$$$\text{proof}(subschemeFunctor) \text{ in opposite}~Y$$$

Lean4

/-- The functor taking an ideal sheaf to its associated subscheme. -/
@[simps]
noncomputable def subschemeFunctor (Y : Scheme.{u}) : (IdealSheafData Y)ᵒᵖ ⥤ Over Y
    where
  obj I := .mk I.unop.subschemeι
  map {I J} h := Over.homMk (IdealSheafData.inclusion h.unop.le)

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