Re: The Category of Semimodules over Semirings

["Fred E.J. Linton" <fejlinton@usa.net>]

On Sun, 16 Mar 2008 09:26:35 AM EDT Jawad Abuhlail <abuhlail@kfupm.edu.sa> 
wrote, in part, on the Subject: The Category of Semimodules over Semirings,

> ...  The category of semimodules had products, equalizers and
> products (however not necessarily coequalizers). 

I must be missing something here. Don't the (say, left-) semimodules
(over a given semiring) constitute an equationally definable class 
of algebras? That is, aren't they determined entirely by operations 
and equations?

If they DO, that is, if they ARE, then the category of them all (together
with their homomorphisms) must, like all such "varietal categories," have 
all (small) limits and colimits, and, in particular, all coequalizers.

Alas, I have little else to offer. Cheers, and Happy St. Paddy's Day,

-- Fred