My supervisor's opinion on this topic seems to be that we would not end at category theory, but that it is a step into the right direction of where to focus our

My supervisor's opinion on this topic seems to be that we would not end at category theory, but that it is a step into the right direction of where to focus our attention. EDIT: For example, my MSc was on the topic of a category equipped with a functor into it. This allows one to construct (parts of, e.g. I haven't done subobject classifiers) a self dual set theory.