List of finite categories

List of finite categories

[Jamie Vicary]

Hi,

Has anyone created a list of all finite categories up to a given size, up
to equivalence? (An easy definition of size would be the number of
morphisms in a skeletalization.)

Best wishes,
Jamie



[For admin and other information see: http://www.mta.ca/~cat-dist/ ]

Re: List of finite categories

[Vaughan Pratt]

On 5/23/2014 2:52 AM, Jamie Vicary wrote:
> Has anyone created a list of all finite categories up to a given size, up
> to equivalence? (An easy definition of size would be the number of
> morphisms in a skeletalization.)


If anyone contemplates doing this, I'd be interested in two independent
variants as well (so four enumerations):

(i) Up to Morita equivalence instead of ordinary equivalence.  When
counting morphisms use the Karoubi envelope (the maximal skeletal member
of the class).

(ii) Bimodules/profunctors K : L -/-> J (sorry, Peter J.), represented
as a category J + L + K where K is the (indexed) set of morphisms from J
to L.  Count morphisms as in the other cases.

Morita equivalence in this case means equivalence of the corresponding
commune categories as defined in

http://boole.stanford.edu/pub/CommunesFundInf2010.pdf

I confess that I don't have a counterpart for the Karoubi envelope, this
would be nice to fix.

Vaughan


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]