2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70451We prove that every finitary polynomial endofunctor of a category $C$ has a final coalgebra if $C$ is locally Cartesian closed, has finite disjoint coproducts and a natural number object. More generally, we prove that the category of coalgebras for such an endofunctor has all finite limits.Category TheoryLogic18B20 (Primary) 18A15, 03G30 (Secondary)text