  We analyse the two definitions of generalized quantifiers for logics of
dependence and independence that have been proposed by F. Engstr\"om, comparing
them with a more general, higher-order definition of team quantifier. We show
that Engstr\"om's definitions (and other quantifiers from the literature) can
be identified, by means of appropriate lifts, with special classes of team
quantifiers. We point out that the new team quantifiers express a quantitative
and a qualitative component, while Engstr\"om's quantifiers only range over the
latter. We further argue that Engstr\"om's definitions are just embeddings of
the first-order generalized quantifiers into team semantics, and fail to
capture an adequate notion of team-theoretical generalized quantifier, save for
the special cases in which the quantifiers are applied to flat formulas. We
also raise several doubts concerning the meaningfulness of the
monotone/nonmonotone distinction in this context. In the appendix we develop
some proof theory for Engstr\"om's quantifiers.
