Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Cogenerating and Finitely cogenerated S-acts   In this paper, cogenerating classes of $S$-acts are introduced as those that
can be used to cogenerate $S$-acts in an appropriate sense. Next, finitely
cogenerated $S$-acts are introduced. Such an $S$-act is then characterized as
one whose socle is finitely cogenerated and large in it. Further, we
investigate the $S$-acts cogenerating $S_S$, or generating the injective
envelope $E(S)$ of $S_S$. This leads us to introduce the classes of cofaithful
and subgenerator $S$-acts as the dual notions of faithful $S$-acts, lying
strictly between the classes of generator and faithful $S$-acts. Ultimately, we
investigate the relationship between the mentioned classes of $S$-acts.

14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph