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: <firstname.lastname@example.org> > > 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..."
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!
In your desperate, never-ending attempts to make me look stupid, it seems to have backfired on you, Jesse.