#18265: Axioms for semigroups: L,R,J,H-trivial, aperiodic
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Reporter: nthiery | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.2
Component: algebra | Resolution:
Keywords: | Merged in:
Authors: Nicolas M. Thiéry | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/nthiery/semigroups/axioms-18265 | d09fe3b47c5d755661ae0053702829985bdf13fc
Dependencies: | Stopgaps:
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Comment (by tscrim):
Replying to [comment:15 nthiery]:
> Replying to [comment:13 tscrim]:
> > - Do we want these to be axioms since these properties for
subcategories do not make as much sense (e.g., for groups, L-trivial =
R-trivial = J-trivial = category consisting only of the trivial group,
correct?)
>
> We want them to be axioms to interact nicely with each other: there
> will be many interesting combinations between the Finite / X-trivial /
> Unital axioms (and more will come, like Regular, ...). In fact
> implementing those was one of my original motivation for implementing
> axioms in Sage :-)
I think we should also add that an inverse R-trivial monoids implies
J/H-trivial.
> Indeed `Groups().XTrivial()` is, well, trivial, so that's boring. But
> this is only polluting the namespace of the Groups() category, not the
> groups themselves, so that's a minimal annoyance.
Considering there is exactly 1 X-trivial group (up to isomorphism), there
won't be any additional pollution from `Parent/ElementMethods` either. So
I agree, minimal annoyance.
> > - Do we want to spend some time trying to beautiful axiom printing
> > (i.e., "J-trivial" instead of "jtrivial")?
>
> This would be cute, indeed. I'll have a quick look if it's trivial to
> do. Otherwise, we can leave it for later; that will be easy to change
> anyway.
Let me know.
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Ticket URL: <http://trac.sagemath.org/ticket/18265#comment:16>
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