Re: Are there exactly 11 categories with 3 arrows?

[Vaughan Pratt <pratt@cs.stanford.edu>]

On 3/26/2010 6:01 PM, Aleks Kissinger wrote:
 > Probably a good exercise to work out the details yourself, but here's
 > a hint. The 1-object case is exactly the same as counting monoids.

With the exception of one category, so is the general case.  It suffices
to identify the odd category out and then put the remainder in bijection
with the monoids of order at most 3 (see Sloane A058129).

For positive integer n, 3 is the least value of n for which the
categories with n arrows cannot be put in bijection with the monoids of
order at most n.

Vaughan


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