On projectively quotient functors

summary:We introduce notions of projectively quotient, open, and closed functors. We give sufficient conditions for a functor to be projectively quotient. In particular, any finitary normal functor is projectively quotient. We prove that the sufficient conditions obtained are necessary for an arbitrary subfunctor $\Cal F$ of the functor $\Cal P$ of probability measures. At the same time, any ``good'' functor is neither projectively open nor projectively closed.