isColimitOfIsWellOrderContinuous'

English

Under an order isomorphism, the IsWellOrderContinuous property is preserved along the transformed shape.

Русский

При изоморфизме порядка свойство IsWellOrderContinuous сохраняется при преобразовании формы.

LaTeX

$$$\text{IsWellOrderContinuous}(F) \Rightarrow \text{IsWellOrderContinuous}(F')$ under order iso$$

Lean4

/-- If `F : J ⥤ C` is well-order-continuous and `h : α <i J` is a principal
segment such that `h.top` is a limit element, then
`F.obj h.top` identifies to the colimit of the `F.obj j` for `j : α`. -/
noncomputable def isColimitOfIsWellOrderContinuous' (F : J ⥤ C) [F.IsWellOrderContinuous] {α : Type*} [PartialOrder α]
    (f : α <i J) (hα : Order.IsSuccLimit f.top) : IsColimit (f.cocone F) :=
  (F.isColimitOfIsWellOrderContinuous f.top hα).whiskerEquivalence f.orderIsoIio.equivalence

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