isPullback — Mathlib

English

Pullback square as defined by pullbackπ f y is indeed a pullback square.

Русский

Квадрат вытягивания, заданный pullbackπ f y, действительно является квадратом вытягивания.

LaTeX

$$$\text{IsPullback}(\mathrm{pullback\u00A0π}(f,y), (\mathrm{pullback}(f).obj(y)).arrow, y.arrow, f)$$$

Lean4

/-- This states that `pullbackπ f y` indeed forms a pullback square (see `Subobject.pullbackπ`). -/
theorem isPullback (f : X ⟶ Y) (y : Subobject Y) : IsPullback (pullbackπ f y) ((pullback f).obj y).arrow y.arrow f :=
  (isPullback_aux f y).choose_spec

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