  Let $X$ be a topologically stratified space, $p$ be any perversity on $X$,
and $k$ be a field. We show that the category of $p$-perverse sheaves on $X$,
constructible with respect to the stratification and with coefficients in $k$,
is equivalent to the category of finite-dimensional modules over a
finite-dimensional algebra if and only if $X$ has finitely many strata and the
same holds for the category of local systems on each of these. The main
component in the proof is a construction of projective covers for simple
perverse sheaves.
