  An outline and summary of four new potential applications of category theory
to OOP research are presented. These include (1) the use of operads to model
Java subtyping, (2) the use of Yoneda's lemma and representable functors in the
modeling of generic types in generic nominally-typed OOP, (3) using a
combination of category presentations and cartesian closed categories to model
structurally-typed OOP, and (4) the use of adjoint functors to model Java
erasure.
