ext_of_isDominant — Mathlib

English

Dominant extension style gives equality of morphisms under a dominant map in the separated setting.

Русский

Подобный доминантный подход даёт равенство морфизмов при доминантной карте в рамках раздельности.

LaTeX

$$ext_of_isDominant_of_isSeparated (∗)$$

Lean4

/-- Suppose `f g : X ⟶ Y` where `X` is a reduced scheme and `Y` is a separated scheme.
Then `f = g` if `ι ≫ f = ι ≫ g` for some dominant `ι`.

Also see `ext_of_isDominant_of_isSeparated` for the general version over arbitrary bases.
-/
theorem ext_of_isDominant [IsReduced X] {f g : X ⟶ Y} [Y.IsSeparated] (ι : W ⟶ X) [IsDominant ι] (hU : ι ≫ f = ι ≫ g) :
    f = g :=
  ext_of_isDominant_of_isSeparated (Limits.terminal.from _) (Limits.terminal.hom_ext _ _) ι hU

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