#10963: More functorial constructions
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Reporter: nthiery | Owner: stumpc5
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-6.2
Component: categories | Resolution:
Keywords: days54 | Merged in:
Authors: Nicolas M. Thiéry | Reviewers: Simon King, Frédéric
Report Upstream: N/A | Chapoton
Branch: | Work issues:
public/ticket/10963-doc- | Commit:
distributive | c718f218fbc726bf3cf7f4c3f20638c9b0c7eea7
Dependencies: #11224, #8327, | Stopgaps:
#10193, #12895, #14516, #14722, |
#13589, #14471, #15069, #15094, |
#11688, #13394, #15150, #15506 |
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Comment (by SimonKing):
Replying to [comment:520 nthiery]:
> It also misses the point of mixin as providing methods but not state.
There is already a way do deal with state, namely make `FixedBaseRing`
into a category and form join categories.
So, the strategy would be this: The current "Category over base ring"
should accept as input no a ring, but a subcategory of the category of
rings. A polynomial ring should be initialised in the category of
"commutative algebras over Category of quotient fields" (say), and should
of course have its own reference to the base ring (say, the rational
field).
Since the parent and element classes only depend on the category of the
base ring (by the current implementation), a category refinement would
probably not be needed. But *if* needed, it would amount to take the join
with the category "`FixedBaseField(QQ)`, perhaps with super-categories
"`FixedBaseRing(QQ)`".
Additional technical problem: We not only have base rings, but (for
bimodules) left and right base rings. Should this be reflected in the
"`FixedBaseBla`" categories as well?
And another complication: We want to have categories expressing the fact
that a field (not just a ring) is acting on the objects, and then want to
compute the join. Is there an easy programmatic way to let an error be
raised when someone tries to compute the join "`Algebras(Fields()) &
FixedBaseRing(ZZ)`"?
--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:521>
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