characterizing cogenerating and finitely cogenerated s-acts

In this paper, we introduce cogenerating classes of s-acts as those that can be used to cogenerate s-acts in an appropriate sense. next, finitely cogenerated s-acts are characterized by the property that their socle is finitely cogenerated and large in the s-act. further, we investigate the s-acts cogenerating ss, or generating the injective envelope e(s) of ss. this leads us to introduce the classes of cofaithful and subgenerator s-acts as the dual notions of faithful s-acts, which lie strictly between the classes of generator and faithful s-acts. ultimately, we study relations between the cogenerating classes, finitely cogenerated s-acts, and the recently introduced new classes of s-acts.