ℤ-Algebroid Structure of the Category of Groups ℤ_n and Its Subprealgebroids

In this study, we show that the category Z of all cyclic groups ℤ_n has a ℤ-algebroid structure. Moreover, we examine and characterize homsets of Z and see that each homset has a cyclic group structure. Furthermore, through narrowing homsets of Z, we obtain subpre-ℤ-algebroids of Z. In particular, for each positive integer t we get a different subpre-ℤ-algebroid Z_t of Z, where Z_1 = Z. As a consequence, we obtain a countably infinite set of (pre)algebroid samples for their use in future studies.