My count is that there are 24 occurrences of this particular combination.
There are other combinations that exist for which a named category is
available - one example is Join(LinearAggregate(S),   finiteAggregate)
which can be replaced with FiniteLinearAggregate(S). One place applicable
would be FiniteLinearAggregateFunctions2.

When I see this in code bases, it is an indicator that this should be
looked at and fixed appropriately.

Hill

On Thu, Feb 22, 2024 at 2:23 AM Ralf Hemmecke <[email protected]> wrote:

> On 2/21/24 15:46, Hill Strong wrote:
> > I have quite a few places in the FriCAS source code the following
> >
> > Join(SemiRng, AbelianMonoid)
> >
> > What would you call this particular algebraic structure?
>
> The name is actually irrelevant. Since it is a Join, it is actually an
> unnamed category in FriCAS that is only there for the purpose of listing
> the exports (probably you have found it places like this:
> https://github.com/fricas/fricas/blob/master/src/algebra/polycat.spad#L21
> or this
> https://github.com/fricas/fricas/blob/master/src/algebra/matcat.spad#L723
> ).
>
> It says nothing more than for functionality that is provided by (for
> example) RectangularMatrixCategory, it is enough, if the coefficient
> domain is a (possibly non-commutative wrt. multiplication) Ring
> (possibly without 1).
>
> It looks as if SemiRng would be enough, but seemingly the existence of
> the additive neutral element 0 is required.
>
> Of course, FriCAS could introduce a name for this, and perhaps some day
> it will, but it seems not necessary now.
>
> I guess, if you are not satisfied with this answer, Waldek will comment
> more on this.
>
> Ralf
>
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