#15801: Categories over a base ring category
---------------------------+----------------------------
Reporter: nthiery | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.2
Component: categories | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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Currently, to construct a category of algebras, we need to specify the
base ring:
{{{
sage: Algebras(QQ)
}}}
A side effect is that the construction of e.g. {{{GF(p)['x']}}} for a
lot of `p`'s in number theoretic calculations triggers the
construction of many parallel hierarchies of categories.
This is a waste because in most situations only the category of the
base ring is relevant. In particular, the generic code provided to
parents/elements/... only depends on the latter.
The purpose of this ticket is to allow for only specifying the
category of the base ring, as in:
{{{
sage: Algebras(Fields())
}}}
with
{{{
sage: Algebras(QQ)
}}}
constructing a subcategory of the former. Then go trough the code,
decide in each case whether we want to use {{{Algebras(QQ)}} or
{{{Algebras(Fields())}}}, and update the doctests accordingly. In most
case, the latter idiom will be preferable, unless we need some
operation on the category itself.
This would fix the regression noted on #15792 and made worse by
#10963.
Further features for this ticket or follow-up tickets would be to:
- make {{{Modules(...)}}} into a covariant functorial
constructions. This would give a proper framework for the feature
{{{Modules(QQ)}}} -> {{{VectorSpaces(QQ)}}} instead of having to
tackle it with a special hack.
- implement a {{{PolynomialRings(...)}}} covariant functorial
construction.
--
Ticket URL: <http://trac.sagemath.org/ticket/15801>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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