pullbackArrows — Mathlib

English

There is an equivalence between IsLimit((E.map F).multifork P) and IsLimit(E.multifork (F.op ⋙ P)).

Русский

Существует эквивалентность между IsLimit((E.map F).multifork P) и IsLimit(E.multifork (F.op ⋙ P)).

LaTeX

$$$IsLimit\big((E.map F).multifork P\big) \simeq IsLimit\big(E.multifork (F^{op} \circ P)\big)$$$

Lean4

theorem pullbackArrows {X Y : C} (f : X ⟶ Y) (R : Presieve Y) [R.HasPullbacks f] :
    (Presieve.pullbackArrows f R).FactorsThruAlong R f :=
  by
  intro Z g ⟨W, b, hb⟩
  have := R.hasPullback f hb
  refine ⟨_, pullback.fst _ _, b, hb, pullback.condition⟩

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