Dear Ellis I also had this question when i started with category theory but i was satisfied with the Yoneda lemma. Now thanks to your question i know more theorems to answer this. I don't think you can get a better answer than the replied suggestions. However there is also higher category theory. The interesting point would now be to generalize: What are the coresponding theorems for strict/weak n-categories? I plan to at least ask for and suggest a higher dimensional Yoneda lemma. The other adjoints preserving limits theorem is also interesting to generalize. But here as far as i know there is no concept of adjoint for 3-categories and higher up. I am more uncertain as to limits, but i have not seen limits in n-categories defined in the graceful style of limits in 1-categories. Best regards Rafael Borowiecki [For admin and other information see: http://www.mta.ca/~cat-dist/ ]