Homotopy Type Theory, Higher Category Theory

My interests lie in category theory and its various ramifications. My master's thesis was concerned with connecting two concepts from category theory. One of these was that of a monad, which is directly applicable to functional programming. As I have always been interested in the foundations of mathematics and computation, homotopy type theory would suit me very well as a research topic so I aim to expand the analogy between monads and semigroupads, to yield a notion of idempotent completion of 2-categories, which would fully justify my choice of research on what an idempotent in a 2-category should constitute. Additionally, it would be interesting to examine how similar this notion of idempotent completeness of 2-categories