On Nov 7, 10:08 am, "Jesse F. Hughes" <je...@phiwumbda.org> wrote:
> Okay, so you're saying that this wasn't an axiomatization of category, > but simply a question you had about whether this ought to be an > axiomatization of category? >
Yes. In the same posting, I also put forward the idea of an equivalence relation as an alternative for consideration. In that case, the comp function would map not to individual morphisms, but to equivalence classes of morphisms. If I am not mistaken, you yourself suggested something like that at one point.
> From where I sat, you seemed to be genuinely defending the claim that > composition is non-functional.
Only in the sense that, in some cases, there are multiple, distinct candidates for The Composition of two given morphisms as you are defining a putative comp function for consideration (see my example with f, g, h1 and h2). To define a suitable comp function, it turns out that you need only pick one of those alternatives ("Flip a coin").
> Perhaps I was mistaken. Maybe you were > playing the Socratic role and not intent on defending your > non-functional interpretation. > > If so, perhaps the fault is mine, though I doubt it. You sure looked to > me like you were seriously suggesting that composition is > non-functional. I wonder if others thought the same thing. >
I can see where the confusion might arise. And maybe it still exists.