Re: "Semi-additive" seems to be it

["George Janelidze" <janelg@telkomsa.net>]

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
>
>
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