comapIso — Mathlib

English

The same kernel-comap/subscheme compatibility as in 37055, but stated with a simplification marker for automated reasoning.

Русский

Та же совместимость comapIso_inv_subschemeι через ядро и вложение подсхемы, оформленная как упрощение.

LaTeX

$$$(I.comapIso f).inv \cdot (I.comap f).subschemeι = pullback.fst _ _$$$

Lean4

/-- The subscheme associated to the pullback ideal sheaf is isomorphic to the fibred product. -/
def comapIso (I : Y.IdealSheafData) (f : X ⟶ Y) : (I.comap f).subscheme ≅ pullback f I.subschemeι :=
  (asIso (pullback.fst f I.subschemeι).toImage).symm

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