prodLift₁ — Mathlib

English

The prodLift construction factors through curry to yield an identity on W₂.Q after flipping.

Русский

Конструкция prodLift факторизуется через карри, давая тождество на W₂.Q после разворота.

LaTeX

$$$W_2.Q \\cdot (\\text{curry.obj } F)^{\\text{flip}} = (\\text{prodLift}_1 F hF)^{\\text{flip}}$$$

Lean4

/-- Auxiliary definition for `prodLift`. -/
noncomputable def prodLift₁ [W₂.ContainsIdentities] (hF : (W₁.prod W₂).IsInvertedBy F) : W₁.Localization ⥤ C₂ ⥤ E :=
  Construction.lift (curry.obj F)
    (fun _ _ f₁ hf₁ =>
      by
      haveI : ∀ (X₂ : C₂), IsIso (((curry.obj F).map f₁).app X₂) := fun X₂ => hF _ ⟨hf₁, MorphismProperty.id_mem _ _⟩
      apply NatIso.isIso_of_isIso_app)

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