lift — Mathlib

English

Congruence of lifts: if two morphisms f and f1, two morphisms g and g1 are equal under equations e_f, e_g, then their lifts are equal.

Русский

Сходимость подъемов: если f = f1 и g = g1 по равенствам e_f, e_g, то подъемы равны.

LaTeX

$$$ Eq(f,f_1) \to Eq(lift(f,g,H'), lift(f_1,g_1, H')) $$$

Lean4

/-- The universal property of open immersions:
For an open immersion `f : X ⟶ Z`, given any morphism of schemes `g : Y ⟶ Z` whose topological
image is contained in the image of `f`, we can lift this morphism to a unique `Y ⟶ X` that
commutes with these maps.
-/
def lift (H' : Set.range g.base ⊆ Set.range f.base) : Y ⟶ X :=
  have := pullback_snd_isIso_of_range_subset f g H'
  inv (pullback.snd f g) ≫ pullback.fst _ _

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