Hi Mark,
On 2012-04-20, Mark Shimozono <[email protected]> wrote:
> You had mentioned the functor that, when applied to a group, creates
> the group algebra.
> I know about the algebra method for sets. Can one also get induced
> algebra morphisms this way too,
> as the name "functor" suggests should be possible?
Probably not - simply since (as much as I know) group algebras aren't
fully implemented in Sage, yet.
Also, what functor is it that you/Nicolas are/is talking about? I would
expect it to be a construction functor and thus provided in the module
sage.categories.pushout, but it isn't there.
Anyway. If there are problems with applying a functor to objects or
morphism, please look at the documentation of
sage.categories.functor.Functor, which states:
* When defining a sub-class, the user should not implement a call
method. Instead, one should implement three methods, which are
composed in the default call method:
* "_coerce_into_domain(self, x)": Return an object of "self"'s
domain, corresponding to "x", or raise a "TypeError".
* Default: Raise "TypeError" if "x" is not in "self"'s domain.
* "_apply_functor(self, x)": Apply "self" to an object "x" of
"self"'s domain.
* Default: Conversion into "self"'s codomain.
* "_apply_functor_to_morphism(self, f)": Apply "self" to a
morphism "f" in "self"'s domain. - Default: Return
"self(f.domain()).hom(f,self(f.codomain()))".
Hence, if the functor fails to provide induced morphisms, then one
should look at _apply_functor_to_morphism, or one should try to make
A.hom(f,B)
work, where f is a group homomorphism from group a to group b, and
where A and B are the group algebras of a and b, respectively. If the
latter works, then application of the functor should work as well.
Best regards,
Simon
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