Take a look at my response to the other guy. I clarified my point with a thorough example. Please note that I was somewhere else and on the phone when I typed my initial response so forgive me for the brevity and lack of clarity. Hopefully the new response will clear things up.

Anyway...

I think theres a good chance that you simply aren't grasping what the category theory fans are saying. Hopefully you grasped what I'm saying.