Hello again, I have thought a while about morphisms and although I had written down in my paper that a functor and also a natural transformation are also morphisms, but in a different category, I now am not sure anymore of this. If you see everything(objects and morphisms) as dots and arrows, and some arrows and some dots are just some more complex than others, then this holds, but is that legal? Intuitively seen, it is. According to some paper, morphisms are not like functions, in that you can apply some morphism to an object, but that you can only compose them. But I would say that if you have the morphism f:a->b, that is a arrow from dot a to dot b. That there clearly is a notion of following that arrow, in effect applying a function. And suppose there is the following path of morphisms: a---->b---->c---->d, with a..d are dots. Then I would say there are three functions(constructed by composition)(in fact more, because of identity mapping) from a that when followed give new objects. This following of arrows, looks a lot like general function application, as in f(x) = 2x for example. It's btw quite hard to write the essence of monads down in a clear and precise way. I hope you can give some feedback on the above. Ragards, Ron P.S. The question about multiplication still stands. Probably multiplication is a set of laws defined on a mathematical object that must hold. And for each mathematical object there is such definition. Is this correct? __________________________________ Do you Yahoo!? Friends. Fun. Try the all-new Yahoo! Messenger. http://messenger.yahoo.com/