Is this question even for this lecture (I wonder :) ) First let me say hi from Amsterdam, and complement all of you on this magnificent project. Things are slowly clicking in my mind, but now I am pondering this question (after watching this lecture hence) if I have carrier i and structure map F i -> i as my initial algebra and another algebra F a -> a and they commute (as they would) does a needs to be of the same type as i? Or could it be completely different. Thanks in advance for any answer. Regards Laurens