* List of finite categories
@ 2014-05-23 9:52 Jamie Vicary
2014-05-24 5:11 ` Vaughan Pratt
0 siblings, 1 reply; 2+ messages in thread
From: Jamie Vicary @ 2014-05-23 9:52 UTC (permalink / raw)
To: Categories list
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/ ]
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* Re: List of finite categories
2014-05-23 9:52 List of finite categories Jamie Vicary
@ 2014-05-24 5:11 ` Vaughan Pratt
0 siblings, 0 replies; 2+ messages in thread
From: Vaughan Pratt @ 2014-05-24 5:11 UTC (permalink / raw)
To: Categories list
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/ ]
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