From: bourn@lmpa.univ-littoral.fr
To: "George Janelidze" <janelg@telkomsa.net>
Cc: "Categories list" <categories@mta.ca>
Subject: Re: "Semi-additive" seems to be it
Date: Mon, 9 Jan 2012 09:47:18 +0100 (CET) [thread overview]
Message-ID: <E1RkJol-0006bs-In@mlist.mta.ca> (raw)
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
I agree with
> May I try to protest against "plurality"?
>
> My reason of suggesting "half-" and not "semi-" is "semi-abelian". I
understand that "semi-" is suggested by "semigroup", but "semi-abelian"
was
> suggested by "semidirect products". Note that "semidirect products" are
defined categorically and a semi-abelian category is abelian if and only
if
> its semidirect products coincide with direct (that is, cartesian) products.
>
> Similarly, if a category with finite coproducts merely has semidirect
products, then it is additive if and only if its semidirect products
coincide with direct products.
>
> Another reason against
>
> "semi-additive = enriched in commutative monoids + has finite products"
>
> is that we do not want to identify monoids with semigroups, do we?
>
> And, surely, instead of saying that
>
> "While the category of commutative monoids is a motivating example of a
semi-additive category, the category of commutative semigroups is not
semi-additive"
>
> it is much better to say that
>
> "Semi- refers to semidirect products and not to semigroups".
>
> I hope to get support even from those who already made the opposite
suggestion...
>
> George
>
> P.S. Well, I always try to respect old terminology, but sometimes (what can
> we do?) it is better to change it. By the way, many years ago Dmitrii
Raikov
> introduced another notion of "semi-abelian". As it turned out with help
of
> Yaroslav Kopylov, that Raikov semi-abelian means
>
> additive + regular + coregular
>
> It is an important notion with interesting examples, but what we call
semi-abelian today seemed to be so much more suitable to call
> "semi-abelian"!
>
>
> --------------------------------------------------
> From: "Michael Barr" <barr@math.mcgill.ca>
> Sent: Saturday, January 07, 2012 2:38 PM
> To: "Categories list" <categories@mta.ca>
> Subject: categories: "Semi-additive" seems to be it
>
>> Thanks for all the replies, but while there was consensus,
>> "semi-additive"
>> got a plurality and we will go with that.
>> Michael
>> --
>> Any society that would give up a little liberty to gain a little
security will deserve neither and lose both.
>> Benjamin Franklin
>> [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
>
>
>
> [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
>
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
next reply other threads:[~2012-01-09 8:47 UTC|newest]
Thread overview: 11+ messages / expand[flat|nested] mbox.gz Atom feed top
2012-01-09 8:47 bourn [this message]
2012-01-09 19:39 ` Robin Cockett
2012-01-13 23:36 ` What about biproducts? George Janelidze
2012-01-14 20:12 ` Michael Barr
2012-01-14 21:13 ` rlk
2012-01-10 2:35 ` "Semi-additive" seems to be it Ross Street
2012-01-10 15:07 ` Todd Trimble
[not found] ` <E1Rm52K-0002ko-Nm@mlist.mta.ca>
2012-01-16 9:41 ` What about biproducts? Vaughan Pratt
-- strict thread matches above, loose matches on Subject: below --
2012-01-07 12:38 "Semi-additive" seems to be it Michael Barr
2012-01-07 19:48 ` George Janelidze
2012-01-08 21:14 ` FEJ Linton
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