> Yes. In Categorial Language, I have functors from the category of multisets
> with bijections to the category of sets with bijections, I
> guess.
Maybe.
> Unfortunately, BLL use "multiensemble" (in french, what do they use in
> english?) for something different, namely, a k-tuple of sets. A k-multisorted
> species is a functor from the category of k-tuples of sets and bijections to
> the category of sets with bijections...
Ha, it seems you stepped over the same problem as me. ;-) For some time
I was wondering, why they call something like "k-tuple of sets" a
"k-multiset". I could not see equal elements. After a while I realized
that if you have a BLL-multiset U1+U2+...+Uk and factor out any
permutations of the components, you basically make all elements of U1
equal (same for U2,...,Uk). And that is a multiset as we are used to it.
> So, my thing seems to be quite disjoint from multisort species. Only certain
> cases of isomorphismtypes coincide, as you have noted. (But I didn't check)
>>> In particular, I think generating labelled structures of several sorts is
>>> not covered by my approach.
>> Only through mapping (multisort) labels to integer, generating iso types and
>> mapping back.
>
> ???
Let us just take the multiset {1^3, 2^2} which you can treat.
If I have a BLL-multiset ({a,b,c},{A,B}), I simply map it to your
multiset and then replace 1 by a and 2 by A. (But perhaps, b, c and B
should also appear in the result.)
>> In fact, I would not throw away your code, because basically you implemented
>> the ground algorithm which must be adapted to multisort. (Whatever we decide
>> what "multisort" should look like in AC.)
>
> I didn't intend to throw away my code. I think it's quite ok. And in fact,
> very
> likely we will need - to generate isomorphismtypes of compositions of
> multisorted species - functors from the category of k-tuples of multisets to
> the category of sets...
Rather, a multisort species M is a functor M: B^k -> B. (k-tuples of
"sets", not "multisets")
>> Of course, one could say that L is the disjoint union of all sorts and have
>> just one L in the argument of CombinatorialSpeciesCategory, but I somehow
>> have the feeling there will go something wrong when it comes to functorial
>> composition F \square (G_1, ..., G_n). Not that I have completely thought
>> that through, but I guess that changing the argument from LabelType to
>> Tuple(LableType) would be more appropriate.
> I don't think so, but I guess, only time will tell.
How does M: B^k -> B look like to you?
Ralf
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