On Tuesday, November 6, 2012 12:55:34 PM UTC-5, Dan Christensen wrote: > On Nov 6, 12:08 pm, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: > > > Dan Christensen <Dan_Christen...@sympatico.ca> writes: > > > > On Nov 6, 11:50 am, Frederick Williams <freddywilli...@btinternet.com> > > > > wrote: > > > >> Dan Christensen wrote: > > > > > > >> > We seem to settled on a list of 10 axioms. (Special thanks to Aatu and > > > >> > Rotwang for their suggestions.) > > > > > > >> I do hope Aatu and Rotwang won't mind being implicated. > > > > > > > Aatu confirmed my intuition about arbitrarily selecting a composition > > > > in the rare case of multiple, distinct possibilities. Rotwang pointed > > > > out a problem with Axiom 3, which I fixed. > > > > > > I think you mean: Aatu corrected your stupid misconception that > > > composition wasn't functional -- just as many other people did -- but > > > you arbitrarily suggested Aatu as "confirming" something that you just > > > had butt-wrong. > > > > Asked, "What to do when there are multiple, distinct morphisms from > > which to choose the composition?" Aatu replied, "We flip a coin."
Are you talking about constructing a category from scratch, or are you starting with a particular category?
If you are trying to construct a category from a collection of arrows, then yes, there are many ways you can choose the composition. This is equivalent to choosing the composition rule.
The composition rule is one of the things that define what that particular category is.
It is wrong, in fact, non-sensical, to say that given a category, there are multiple choices for a composition.
> > > > Really, Jesse, it is time to deal with these massive insecurities that > > seem to be eating away at you. > > > > Dan > > Download my DC Proof 2.0 software at http://www.dcproof.com