On Nov 7, 9:28 am, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: > Dan Christensen <Dan_Christen...@sympatico.ca> writes: > > On Nov 7, 6:53 am, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: > >> Dan Christensen <Dan_Christen...@sympatico.ca> writes: > >> > On Nov 6, 6:18 pm, "Jesse F. Hughes" <je...@phiwumbda.org> wrote: > >> >> You didn't say that. You said earlier today that composition was not > >> >> functional. > > >> > [snip] > > >> > Pay attention, Jesse. In every version of my definition of category, > >> > composition was presented as a function. For every ordered pair of > >> > compatible morphisms, there would exist a unique morphism that was > >> > their composition. After posting my latest version, I began to openly > >> > question it here, wondering if indeed such a unique morphism always > >> > existed. It doesn't always, but, as Aatu pointed out in effect, you > >> > arbitrarily pick one of the alternatives for your definition of > >> > compositions to maintain functionality -- "We flip a coin." So, my > >> > latest definition of stood. > > >> Wow. You are either a liar or have a mental condition that represses > >> all memory of your errors. > > >> Look at message https://groups.google.com/group/sci.math/msg/87d7499de8ad28de?dmode=s... > >> Message-ID: <60c69813-35f2-4bc7-8fb2-f81b8e0ea...@h9g2000yqd.googlegroups.com> > > >> Here, we find axiom 2: > > >> 2 ALL(f):ALL(g):ALL(h):[f @ mor & g @ mor & h @ mor => [(f,g,h) @ > >> comp > >> <=> cod(f)=dom(g) & dom(f)=dom(h) & cod(h)=cod(g)]] > > > A little creative editing, Jesse? In the text just prior to that (see > > link), I wrote: > > > "I also think there may be a larger problem with the functionality of > > composition. Suppose, for example, that f is morphism from object A to > > object B, that g is morphism from B to C, and that h1 and h2 are > > distinct morphisms from A to C. Then comp(g,f) as defined here could > > be either h1 or h2, could it not? Should we define some equivalence > > relation on mor. Should comp be seen as a non-functional mapping from > > mor x mor to mor? How about something like..." > > What the fuck are you on about? Axiom 2 stated above is clearly about a > non-functional relation called comp. This excerpt supports that claim. > You gave an explicit axiom in which composition was non-functional. >
> > Aatu, it seems, kicked your ill-informed butt with his "We flip a > > coin" remark. You no longer claim I was "lying" about that. That's > > real progress. But here, it seems you are reduced to deliberately > > taking my words out of context and, again, calling me a liar! > > Aatu kicked my ill-informed butt?
> I think not. Why not ask him if > that's what he thinks? > > I think that his comment is utterly misleading (though, I have not > doublechecked the context, so I am prepared to eat those words).
> We do > not "flip a coin" to define composition.
Again, that was his reply to my question, "What to do when there are multiple, distinct morphisms from which to choose the composition?" (see link above)
> There are two distinct > categories involving the objects and morphisms you describe. They are > distinct because they have different rules of composition (in fact, I > recall Aatu said something like this, so coin-flipping seems mighty odd > to me). But I'll let Aatu explain his use of that term if he cares to. > > Why not ask Aatu if he thinks that he and I have any disagreement on the > role of composition in defining a category? > > As far as taking your words out of context, you said: > > In every version of my definition of category, composition was > presented as a function. > > Axiom 2 is a version of your definition of category in which composition > was explicitly non-functional. >
Pay attention, Jesse. Once again, this was just part of my question that you so unwisely snipped in your vain attempt to discredit me.
> > In your desperate, never-ending attempts to make me look stupid, it > > seems to have backfired on you, Jesse. > > Oh, yeah. It's mighty embarrassing for me, I can tell you. >