On 17/01/07, Brian Hulley
Ok I understand it now, because David has just clarified offlist the thing that puzzled me about the diagram: namely that morphisms have an individuality of their own that isn't fully determined by the lhs and rhs of the arrow like the relationship between a function and its type.
I've written a bit more, moved things around and just generally made the intro section clearer. Your troubles have been addressed with an explanatory sentence that gives sin and cos as examples of morphisms with the same source and target objects but that are different. We now deal with composition a bit better too; when we're defining a category we briefly mention composition but the closure under the composition operator is now defined and exemplified alongside the other two laws. Thanks, Brian, for your input, it's been valuable. I hope everything's clear now. -- -David House, dmhouse@gmail.com