Category Theory: a possible tool for philosophy?

As we know, applying mathematical logic and set theory to philosophical problems was all the rage during the twentieth century. With the rise of modern cognitive science we better understand how the mind creates philosophy and mathematics. That understanding has at the least made philosophies based upon logic and set theory problematic.

However, over the past week or so, I have been wondering if applying category theory to philosophical problems might not produce some results. That does no alleviate the need for understanding the metaphors and metonyms underlying category theory, but it might be a useful tool all the same.