  We give conditions on a finitary endofunctor of a finitely accessible
category to admit a final coalgebra. Our conditions always apply to the case of
a finitary endofunctor of a locally finitely presentable (l.f.p.) category and
they bring an explicit construction of the final coalgebra in this case. On the
other hand, there are interesting examples of final coalgebras beyond the realm
of l.f.p. categories to which our results apply. We rely on ideas developed by
Tom Leinster for the study of self-similar objects in topology.
