This paper presents the way of integrating various mathematical structures into one system that will result in the improvement of academic knowledge and liberate more useful applications. The work establishes a single approach, which considers groups, rings, fields, modules, and lattices in an inclusive algebraic perspective by applying universal algebra and category theory. This can be seen as such that it is easier to map morphisms and representation theories that retain significant algebraic properties the same across structures. The proposed framework holds a great potential to improve such area as algebraic topology, cryptography, and quantum algebra through the provision of new ideas and simplification of the processes. The issues that may arise and how this unified theory can be extended in the future are also discussed.