#16340: Infrastructure for modelling full subcategories
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Reporter: nthiery | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: categories | Resolution:
Keywords: full | Merged in:
subcategories, homset | Reviewers: Darij Grinberg,
Authors: Nicolas M. Thiéry | Travis Scrimshaw
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/categories/full_subcategories-16340|
d4c7a88563a397291b6cd5ddadb8f574cc1eedb5
Dependencies: | Stopgaps:
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Comment (by nthiery):
Replying to [comment:40 pbruin]:
> OK, but what I meant is that this notion depends on what supercategories
of `C` have been defined, not just on `C` itself.
>
> Certainly, but this relies on the the implementation choice of defining
`Magmas().Unital()`. I admit this may be a slightly silly example, but I
could imagine a different scenario where the person implementing these
categories did not think anyone would need unital magmas, and hence chose
to define `Unital()` relative to a more specific category, which in an
extreme case could be `Rngs()`. In that case `Rings() = Rngs().Unital()`
would have been a structure category, while being mathematically exactly
the same as the actual `Rings()`.
Fair enough: this is indeed not something purely about the abstract
(lattice of) mathematical categories, but about whatever subset has
been actually modeled in Sage. It's not so bad though, since this does
not depend on how the categories have been implemented (e.g. through
axioms or not); just on which categories are implemented or not.
In the above scenario, `Rings` would at first be a structure category;
and then, when the definition of the `Unital` axioms gets lifted up to
some higher category like `Magmas`, Sage would learn that the
structure actually comes from some higher category. That's fine given
the specs about negative answers for "X.is_full_super_category(Y)".
In general, when adding new categories and "moving structure up", one
indeed needs to update the "additional structure" methods of the lower
categories accordingly. Though if one forgets to do it, it should just
cause a lack of new feature, rather than bugs. So we are on the safe
side.
Cheers,
Nicolas
--
Ticket URL: <http://trac.sagemath.org/ticket/16340#comment:46>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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