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

Key Points

• The aim is to establish the ℤ-algebroid structure of the category of cyclic groups and identify their subpre-ℤ-algebroids.
• Characterize homsets within the category of cyclic groups ℤ_n.
• Identify cyclic group structures for each homset.
• Narrow down homsets to derive subpre-ℤ-algebroids.
• Define specific subpre-ℤ-algebroids for each positive integer t.
• Demonstrated that the category Z has a ℤ-algebroid structure.
• Established that each homset in Z has a cyclic group structure.
• Obtained distinct subpre-ℤ-algebroids for each positive integer t, including Z_1 = Z.
• Created a countably infinite set of (pre)algebroid samples for future studies.