toΓSpecCApp — Mathlib

English

Characterizes when a morphism between the basic open structure maps coincides with the canonical CApp map via the Away-lift property of the localization.

Русский

Характеризует равенство морфизмов через свойство Away-локализации.

LaTeX

$$$toΓSpecCApp_iff: (f =) f = X.toΓSpecCApp(r) \Longrightarrow (toOpen \circ f) = ..., $$$

Lean4

/-- Define the sheaf hom on individual basic opens for the unit. -/
def toΓSpecCApp :
    (structureSheaf <| Γ.obj <| op X).val.obj (op <| basicOpen r) ⟶ X.presheaf.obj (op <| X.toΓSpecMapBasicOpen r) :=
  -- note: the explicit type annotations were not needed before
    -- https://github.com/leanprover-community/mathlib4/pull/19757

  CommRingCat.ofHom <|
    IsLocalization.Away.lift (R := Γ.obj (op X)) (S := (structureSheaf ↑(Γ.obj (op X))).val.obj (op (basicOpen r))) r
      (isUnit_res_toΓSpecMapBasicOpen _ r)

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