#18044: Implement categories for super algebras/modules
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Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.6
Component: categories | Resolution:
Keywords: super | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/categories/super_categories-18044|
b29650b87b103a465d66de189182a0e7dcf4fde9
Dependencies: | Stopgaps:
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Comment (by tscrim):
I'm not happy with this because of how certain things in the category
hierarchy are respected, even in this new version. In particular:
{{{
sage: C = HopfAlgebras(ZZ).WithBasis().Super(); C
Category of super hopf algebras with basis over Integer Ring
sage: sorted(C.super_categories(), key=str)
[Category of hopf algebras with basis over Integer Ring,
Category of super algebras over Integer Ring,
Category of super algebras with basis over Integer Ring]
}}}
I don't know a way around this currently...
However I'm starting to wonder if this is what we want. If we want two
notions of super, the first is via a functorial construction for things
like modules and algebras (and rings once the graded versions get
implemented), and for other things if we want the `Super` call to go to a
`Category_over_base_ring` subclass. Mainly the first examples satisfy the
conditions of the regressive covariant functorial construction, but the
others, like Hopf and Lie algebras, don't. Doing things this way also seem
like they will simplify the implementation as a fringe benefit. Thoughts
(inc. from Nicolas)?
--
Ticket URL: <http://trac.sagemath.org/ticket/18044#comment:16>
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