when do we considered a group to be a set
Group (mathematics) Many groups are simultaneously groups and examples of other mathematical structures. In the language of category theory, they are group objects in a category, meaning that they are objects (that is, examples of another mathematical structure) which come with transformations (called morphisms) that mimic the group axioms. For example, every group (as defined above) is also a set, so a group is a group object in the category of sets.
Primary and secondary groups People in a secondary group interact on a less personal level than in a primary group. Since secondary groups are established to perform functions, peopleâ€™s roles are more interchangeable. A secondary group is one you have chosen to be a part of. They are based where many people can meet close friends or people they would just call acquaintances. Secondary groups are groups in which one exchanges explicit commodities, such as labour for wages, services for payments, etc. Examples of these would be employment, vendor-to-client relationships, etc.