indexCone — Mathlib

English

The constructed index cone is a limit cone for the indexFunctor.

Русский

Построенная индексная коника образует предел для indexFunctor.

LaTeX

$$$\\text{indexCone}(hC) \\text{ is a limit cone for } \\text{indexFunctor}(hC)$$$

Lean4

/-- The limit cone on `indexFunctor` -/
noncomputable def indexCone (hC : IsCompact C) : Cone (indexFunctor hC)
    where
  pt := @Profinite.of C _ (by rwa [← isCompact_iff_compactSpace]) _ _
  π := { app := fun J ↦ TopCat.ofHom (π_app C (· ∈ unop J)) }

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