From: Vaughan Pratt <pratt@cs.stanford.edu>
To: Categories list <categories@mta.ca>
Subject: Re: List of finite categories
Date: Fri, 23 May 2014 22:11:29 -0700 [thread overview]
Message-ID: <E1WoO1b-0002hv-Dt@mlist.mta.ca> (raw)
In-Reply-To: <E1Wo0vA-0002JU-9c@mlist.mta.ca>
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/ ]
prev parent reply other threads:[~2014-05-24 5:11 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2014-05-23 9:52 Jamie Vicary
2014-05-24 5:11 ` Vaughan Pratt [this message]
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