27 Mar
2010
27 Mar
'10
2:03 a.m.
On Fri, 26 Mar 2010, at 08:09:06 PM EDT, Mark Spezzano <mark.spezzano@chariot.net.au> asked:
Are there exactly 11 categories with 3 arrows?
Some gentle hints, without giving away the answers:
... I need to cover three possibilities:
a) One object with three arrows. How many are there of these?
That's the heart of the problem: how many monoid structures can be imposed on the identity and the two non-identity arrows?
b) Two objects with three arrows. How many are there of these?
Where can the single non-identity arrow be?
c) Three objects with three arrows. ... the answer to this ... is 1 ...
Agreed. HTH. Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]