Monads and Algebraic Structures

This expository paper introduces the concept of monads and explores some of its connections to algebraic structures. With an emphasis on the adjoint functors that naturally participate in our conclusions, we justify how monads give us a distinct, ‘categorical’ way of discussing common structures such as groups and rings. In the final section, we consider a key example of how looking at structures this way is useful, by converting the problem of finding a natural way to combine algebraic structures to one of understanding a proper interaction between their relevant monads. We assume from the reader a familiarity with the basic notions of category theory.