English
The index cone is built as a limit cone over the indexFunctor using the compactness of C.
Русский
Индексная конусность строится как предел над индекс-фанктором с использованием компактности C.
LaTeX
$$$\\text{indexCone}(hC):\\; \\text{Cone}(\\text{indexFunctor}(hC))$$$
Lean4
/-- The functor from the poset of finsets of `ι` to `Profinite`, indexing the limit. -/
noncomputable def indexFunctor (hC : IsCompact C) : (Finset ι)ᵒᵖ ⥤ Profinite.{u}
where
obj
J :=
@Profinite.of (obj C (· ∈ (unop J))) _
(by rw [← isCompact_iff_compactSpace]; exact hC.image (Pi.continuous_precomp' _)) _ _
map h := TopCat.ofHom (map C (leOfHom h.unop))