Ralf Hemmecke <[EMAIL PROTECTED]> writes: > Of course there must be one. \emptyset is an object in B and in a category > there is always the 1 arrow from an object to itself.
OK, that's a good argument for thinking in caegories... > >>> What is G[\sigma]? Ah, sure, it is a permutation in some S_m. > >>> First question: what is m? > >> The only good choice is m=\card G[0]. And to be functorial > >> G[\sigma] must be the identity permuation of S_m. > > I just wanted to look that up. OK, I did: one can say (although I > > don't really have a good argument for that) that the sigma above is > > the identity on the empty set... > > No. G[\emptyset] is not necessarily empty. So the G transports the arrow > > 1: \emptyset -> \emptyset to G[1]: G[\emptyset] -> G[\emptyset]. And the > latter > is most certainly the identity on G[\emptyset], because G is a functor. But that's exactly what I meant to say. (I didn't say that G[\emptyset]=\emptyset, only that \sigma would be the identity on the empty set) > > Note that axiom says lcm(0,n)=0 for any n. > > I don't think that is important since you suggested to take > > n := lcm([i for i in 1..#p | p.i ~= 0]); > > and I would have to compute the lcm of the empty list. That is more > interesting. :-) I'd vote for zero. You see, I think that lcm(0,n)=0 for any n is somewhat problematic, since 0 is a multiple of any number, so why don't we put lcm(n,m)=0 for any n and m? > >> So I would be happy if someone could confirm my thinking. confirmed? > > Thank you? ;-) ? ;-) Martin ------------------------------------------------------------------------- Take Surveys. Earn Cash. Influence the Future of IT Join SourceForge.net's Techsay panel and you'll get the chance to share your opinions on IT & business topics through brief surveys-and earn cash http://www.techsay.com/default.php?page=join.php&p=sourceforge&CID=DEVDEV _______________________________________________ Aldor-combinat-devel mailing list Aldor-combinat-devel@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/aldor-combinat-devel
