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.
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.