coconePointwiseProduct — Mathlib

English

Under the same hypotheses as injectivity, colimitLimitToLimitColimit F is surjective.

Русский

При тех же условиях отображение colimitLimitToLimitColimit F сюръективно.

LaTeX

$$colimitLimitToLimitColimit F is surjective$$

Lean4

/-- The inclusions `(F s).obj (k s) ⟶ colimit (F s)` induce a cocone on `pointwiseProduct F` with
cone point `∏ᶜ (fun s : α) => colimit (F s)`. -/
@[simps]
noncomputable def coconePointwiseProduct : Cocone (pointwiseProduct F)
    where
  pt := ∏ᶜ fun (s : α) => colimit (F s)
  ι := { app := fun k => Pi.map fun s => colimit.ι _ _ }

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