Re: "Semi-additive" seems to be it

[Todd Trimble <trimble1@optonline.net>]

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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