Based on the reactions so far it looks like I'll be going with one of "module" or "bimodule" rather than "bipartite category." A decisive point here was Steve Lack's remark about V-modules, making the point that "abstract module" was less a matter of abstracting the additive structure away than of putting it in by taking V to be additive (whence R-module). So presumably a Set-module would count as an ordinary module, or just a module, by analogy with "an ordinary category, or just a category". (Who'd have guessed the deference paid set theory by the movie "Ordinary People?") (As a digression, this got me to wondering whether abstraction and enrichment could be presented as a suitable adjunction in such cases. The case at hand seems to be a special kind of abstraction: what would such an adjoint be for the notion of 2-cell as an abstract natural transformation, for example? I.e. how would one enrich 2-categories so that the 1-cells became functors and the 2-cells natural transformations?) Peter J. pointed out that bipartite graphs are normally understood to be undirected. However the polarization of the objects makes proscribing negative-to-positive edges entirely equivalent to undirectedness, obvious from the identical matrix formulations of the two kinds of graph. Any difference between bipartite graphs and (Set-)modules would surely come rather from the former disallowing homogeneous edges, those from positive to positive or negative to negative; admitting homogeneous edges breaks the above equivalence. Vaughan Pratt 18-Oct-2004 09:45:40 -0300,1581;000000000000-00000000