#17160: Finitely generated axiom for (mutiplicative) magmas, semigroups,
monoids,
groups
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Reporter: nthiery | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.4
Component: categories | Resolution:
Keywords: | Merged in:
Authors: Nicolas M. Thiéry | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/nthiery/categories/finitely- | f027ce2b5e1abe22d49bcdc96f2cfeebced8fc16
generated-magmas-17160 | Stopgaps:
Dependencies: #10668 |
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Comment (by nthiery):
Replying to [comment:9 tscrim]:
> I think we should make an analogy to `WithBasis` and
> `FiniteDimensional` by having 2 axioms, `WithGeneratingSet` and
> `FinitelyGenerated`. This would give `FinitelyGenerated` a purpose,
> would still allow the current goal of not having to specify the
> enumeration, and allow the option for infinitely generated objects.
I considered this and I agree that this would have the advantage of
being consistent with the basis things. However I don't see what I
would put in the categories with axiom for `FinitelyGenerated` axiom
besides the subcategories with axioms for `WithGeneratingSet`, so this
looks like overkill. Besides,
Categories of finitely generated group with generating set
is not great. I am torn.
Opinions anyone else?
Cheers,
Nicolas
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Ticket URL: <http://trac.sagemath.org/ticket/17160#comment:10>
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