Category Theory and New Classes of Semi Bornological Group

Abstract

Because, the new knowledge put every new structure in category theory. So, became a source of interest for many researchers, to put every new structure in category theory. This motivates us to put the new structures of semibornological group in category. Furthermore, new classes of semibornological group was constructed, which it is a semibornological group with respect to S-bounded maps and semibornological groups with respect to S**-bounded maps. The main important results, every semi bornological group is S-semi bornological group and S**-semi bornological group but the converse is not true. Also, we gave the certain condition for any codomain of S-semi bornological group to be S**-semi bornological group. Additionally, every left (right) translation is S-bornological isomorphism and S**-bornological isomorphism, every bornological isomorphism is S-bornological isomorphism and S**-bornological isomorphism.