terminology

hello: Given a set CC of objects in a topos EE, consider the following property: " X no= empty iff exists C \in CC, hom(C, X) no= empty " example; CC = a set of generators Has (this property) already a name ? If not, can you suggest one ? Any answer will be welcome. (Notice that if CC is a set of points (instead of objects) we say that there are enough points) Thanks Eduardo J. Dubuc