Dear Vaughan, I think it would be a mistake to introduce a new term for these, since there are already several including "profunctor" and "distributor". The additive notions (ring, module, bimodule) generalize well to enriched categories, where it is standard practice to keep the terms module and bimodule without apology. You seem to have rediscovered the set enriched case. Regards, Steve Vickers. Vaughan Pratt wrote:
In my Vancouver talk at CT04 I defined a bipartite category to be a bipolar category with no morphisms from negative to positive objects. (By "bipolar" I mean having two types of objects, positive and negative, or black and white, or manic and depressive.) Robert Seely immediately remarked that this notion already had a name, namely "bimodule," which prompted me to apologize for not being familiar with that abstract usage of the notion.
Since I've always associated modules (and hence bimodules) with rings (and semimodules with semirings), at the very least I'd expect this notion to be called something like "abstract bimodule" to indicate independence of any additive or even semiadditive structure.
Is there an established terminology for this notion? And if not, does anyone have any strong preference between "bipartite category" and "abstract bimodule?" Note that I'll be writing initially for a CS audience, for whom bipartite graphs are a staple.
Vaughan Pratt
18-Oct-2004 09:42:44 -0300,2236;000000000000-00000000