I also find "linear" an attractive option. Just to circumvent any confusion (e.g. with linear in the sense of linear logic, or with the question that may arise: linear over what?), one could say "N-linear" where N is of course the initial rig, as alluded to by Ross. I would hope that "N-linear category" is sufficiently unambiguous to get the meaning across, and sufficiently snappy. Best regards, Todd ----- Original Message ----- From: "Ross Street" <ross.street@mq.edu.au> To: <bourn@lmpa.univ-littoral.fr> Cc: "Categories list" <categories@mta.ca> Sent: Monday, January 09, 2012 9:35 PM Subject: categories: Re: "Semi-additive" seems to be it
Dear All
The concept of category enriched in commutative monoids is a very basic structure and it is important to find a suitable name. I must say I like the term "linear" mentioned by Dominique since the term "k-linear" is commonly used for "enriched in vector spaces over k". Hence there is no conflict if we extend to the case where k is a ring or a rig. Since the natural numbers is the basic example of a rig, we can drop the k in this case.
Best wishes, Ross
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