In this paper we show how a faithful functor, with values in an 0-category, gives rise to a struciure of O-category on its domain. We also prove that the existence of an epi-object in an O-category allows us to define a faithful [unctor with values in P'os and, then, another structure of O-category on it, comparable with the original. Finally, we show that if two faithful functors are related by special natural transformations then they produce comparable siructures of O-category.
