Re: "Semi-additive" seems to be it

[Robin Cockett <robin@ucalgary.ca>]

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


[For admin and other information see: http://www.mta.ca/~cat-dist/ ]