  Recently two different concepts of covers of acts over monoids have been
studied. That based on coessential epimorphisms and that based on Enochs'
definition of a flat cover of a module over a ring. Two recent papers have
suggested that in the former case, strongly flat covers are not unique. We show
that these examples are in fact false and so the question of uniqueness appears
to still remain open. In the latter case, we re-present an example due to Kruml
that demonstrates that, unlike the case for flat covers of modules, strongly
flat covers of S-acts do not always exist.
