hom_eq_lift — Mathlib

English

Every morphism g : X → WidePullback is equal to the lift of its own data: g = lift (g ≫ base) (j ↦ g ≫ π_j) (proof).

Русский

Каждый морфизм g : X → WidePullback равен подъёму от данных g ≫ base и g ≫ π_j.

LaTeX

$$$g = \\mathrm{lift}(g \\gg base, (j \\mapsto g \\gg \\pi arrows j), \\text{proof})$.$$

Lean4

theorem hom_eq_lift (g : X ⟶ widePullback _ _ arrows) :
    g = lift (g ≫ base arrows) (fun j => g ≫ π arrows j) (by simp) := by aesop

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