  For an arbitrary category, we consider the least class of functors con-
taining the projections and closed under finite products, finite coproducts,
parameterized initial algebras and parameterized final coalgebras, i.e. the
class of functors that are definable by $\mu$-terms. We call the category
$\mu$-bicomplete if every $\mu$-term defines a functor. We provide concrete ex-
amples of such categories and explicitly characterize this class of functors
for the category of sets and functions. This goal is achieved through par- ity
games: we associate to each game an algebraic expression and turn the game into
a term of a categorical theory. We show that $\mu$-terms and parity games are
equivalent, meaning that they define the same property of being
$\mu$-bicomplete. Finally, the interpretation of a parity game in the category
of sets is shown to be the set of deterministic winning strategies for a chosen
player.
