isColimitCoconeOfConeLeftOp — Mathlib

Lean4

/-- Turn a limit of `F.leftOp : Jᵒᵖ ⥤ C` into a colimit of `F : J ⥤ Cᵒᵖ`. -/
@[simps]
def isColimitCoconeOfConeLeftOp (F : J ⥤ Cᵒᵖ) {c : Cone F.leftOp} (hc : IsLimit c) : IsColimit (coconeOfConeLeftOp c)
    where
  desc s := (hc.lift (coneLeftOpOfCocone s)).op
  fac s
    j :=
    Quiver.Hom.unop_inj <| by
      simp only [coconeOfConeLeftOp_ι_app, unop_comp, Quiver.Hom.unop_op, IsLimit.fac, coneLeftOpOfCocone_π_app,
        unop_op]
  uniq s m
    w := by
    refine Quiver.Hom.unop_inj (hc.hom_ext fun j => Quiver.Hom.op_inj ?_)
    simpa only [Quiver.Hom.unop_op, IsLimit.fac, coconeOfConeLeftOp_ι_app] using w (unop j)

Похожие утверждения