We consider the Category of Sheaves of Sets. The morphisms are chosen in such a way that a change of the base space is allowed via continuous functions. Following M. M. Clementina, E. Giuli and W. Tholen in "Topology in a Category: Compactness", we define a proper (E, M)­factorization system for morphisms and a closure operator with respect to M. The Stone-Cech compactification is defined for any sheaf (E, p, T) of sets by adapting standard germination processes to construct a sheaf over the Stone-Cech compactification BT (of) T. We prove that the sheaf constructed satisfies a suitable universal property characterizing the Stone-Cech compactification of a sheaf of sets.