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/ ]