Groupoids have entered the OEIS !

[Brendan McKay]

I think using "groupoid" for something that is a quasigroup is just
an error. Unless an eminent source can be found for it, I would
recommend avoiding it completely.

Brendan.

* Benoît Jubin <benoit.jubin at gmail.com> [080517 13:55]:
> Yes, I know that magmas are also called groupoids (for instance... in
> the OEIS!), and that's why I wrote everywhere "groupoids (categories
> all of whose morphisms are invertible)", to avoid confusion.
> 
> For solvable cancellative magmas, I've only seen the term quasigroup.
> A loop being a unital quasigroup.
> 
> By the way, what do you think about adding similar sequences for
> "strongly connected categories" (that is, there exists a morphism
> between every couple - as opposed to pair - of objects) ?
> 
> Sincerely,
> Benoit
> 
> 
> 
> On Fri, May 16, 2008 at 7:45 PM,  <franktaw at netscape.net> wrote:
> > Umm, you should know that the word "groupoid" has multiple meanings.  And
> > (one of) the other one(s) is already in the OEIS.  See A001424 and A001329,
> > or take a look at http://mathworld.wolfram.com/Groupoid.html.
> >
> > In addition to the meanings there, I think I have seen it used for a set
> > with a
> > binary operation which is solvable and cancellable (equivalent conditions
> > for
> > finite examples), but not necessarily associative.  In other words, the
> > operation
> > table is a Latin square.  These are also called quasigroups, or sometimes
> > loops.
> >
> > Franklin T. Adams-Watters
> >
> > -----Original Message-----
> > From: Benoît Jubin <benoit.jubin at gmail.com>
> >
> > Dear SeqFans,
> >
> > I have just contributed six sequences counting finite groupoids
> > (categories all of whose morphisms are invertible):
> > - A140185 (connected groupoids with n morphisms)
> > - A140186 (connected groupoids with n more morphisms than objects)
> > - A140187 (connected groupoids with n times as many morphisms as objects)
> > - A140188 (groupoids with n morphisms and k objects)
> > - A140189 (groupoids with n morphisms)
> > - A140190 (groupoids with m morphisms and (m-n) objects for any m>=2n)
> > The difficulty of counting groupoids is almost entirely in the
> > counting of groups, so that these sequences are not hard to compute
> > from A000001.
> >
> > Maybe this is worth a new entry in the OEIS index ? (and by the way,
> > another entry for categories could be added):
> > categories: A125696, A125697, A125701
> > categories, connected: A125698, A125699, A125700, A125702
> > categories, strongly connected: [sequences to be added]
> > groupoids (categories with inverses): A140188, A140189, A140190
> > groupoids (categories with inverses), connected: A140185, A140186, A140187
> >
> > For the curious, here are two surveys on groupoids:
> > - Ronald Brown, From groups to groupoids: a brief survey
> > http://www.bangor.ac.uk/~mas010/groupoidsurvey.pdf
> > - Alan Weinstein, Groupoids: unifying internal and external symmetry
> > http://www.ams.org/notices/199607/weinstein.pdf
> >
> > Sincerely,
> > Benoit Jubin
> > [my oeis page: math.berkeley.edu/~jubin/oeis.html ]
> >
>