Dear all, I completely agree with Dominique and George!!!! In response to Michael's posting I mentioned privately that Robert Seely, Rick Blute, and I (and others) had, in our work on differential categories, been using commutative monoid enriched categories and, to avoid this mouthful, had just called them "additive". Michael, as I expected did not like this at all as, of course, this means to him Abelian Group enriched. He did not like my suggestion "subtactive" as a replacement for Abelian Group enriched categories either :-) Just to mix things up: as our work is closely related to linear logic the direction of choosing "linear" was not attractive to us either: "linear" in that context means something different again! The stubborn fact is that there are only so many meaningful names. When one does a piece of work one wants to give snappy names to the important concepts in the work. Trying for a globally acceptable snappy name is almost impossible ... so I, for one, am happy to fall back on local naming conventions to replace more cumbersome formal names. And am not above poaching a name if I think it actually describes the concept well in that context. So the point is I am absolutely happy with "commutative monoid enriched category" as formal nomenclature and I am happy if an author wants to do some local naming to make things more readable. Of course, some choices are better than others! I am afraid I also shudder at semi-additive: it suggests commutative semigroup enrichment to me and relegates the concept to being a secondary one ... -robin (Robin Cockett) On Mon, Jan 9, 2012 at 1:47 AM, <bourn@lmpa.univ-littoral.fr> wrote:
Dear all,
I completely agree with George.
By the way, I studied such kind of categories (among others) in: "Intrinsic centrality and associated classifying properties" J. of Algebra, 256, 2002, 126-145. I called them "linear", following Lawvere and Schanuel's "Conceptual Mathematics".
Truly yours,
Dominique
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