#10963: More functorial constructions
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Reporter: nthiery | Owner: stumpc5
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.1
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 | Commit:
Dependencies: #11224, #8327, | eb7b486c6fecac296052f980788e15e2ad1b59e4
#10193, #12895, #14516, #14722, | Stopgaps:
#13589, #14471, #15069, #15094, |
#11688, #13394, #15150, #15506 |
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Comment (by SimonKing):
As indicated above, it seems natural to me that we prefer a "short"
construction (start with a basic category and apply few axioms) over a
"long"
construction (involving a long chain of axioms. This means we would prefer
a
degree order. However, it ''really'' matters what happens after comparing
degrees.
In all examples, I am using a degneglex order.
- Start with the basic categories ''reversedly'' sorted by their name,
followed by the axioms in the ''reversed'' order given by
`sage.categories.categories_with_axioms.all_axioms`. Then, there is only
one
complaint, namely: `Blahs.Unital.Blue` should coincide with
`Blahs.Unital`.
- Start with the basic categories ''directly'' sorted by their name,
followed
by the xioms in the ''reversed'' order given by
`sage.categories.categories_with_axioms.all_axioms`. Then, we
additionally
find: `TestObjects.FiniteDimensional.Unital` should better be provided
by
`Bars.Unital.FiniteDimensional`. Similarly for other educational
examples in
`sage.categories.category_with_axiom`.
- Start with the basic categories ''reversedly'' sorted by their name,
followed by the axioms in the ''direct'' order given by
`sage.categories.categories_with_axioms.all_axioms`. Then the problems
are
similar to the previous case, in the educational examples in
`sage.categories.category_with_axiom`. Such as:
`TestObjects.FiniteDimensional.Unital` should
better be provided by `TestObjects.Blue.FiniteDimensional`.
- Start with the basic categories ''directly'' sorted by their name,
followed
by the axioms in the ''direct'' order given by
`sage.categories.categories_with_axioms.all_axioms`. Again, problems
with
the educational examples in `sage.categories.category_with_axiom`. Such
as:
`TestObjectsOverBaseRing.Unital` should rather be provided as
`TestObjectsOverBaseRing.Blue`.
This result is temporary, as I still seem to miss a couple of category
classes. However, what does it tell us?
On the plus side, all "real" examples work consistently.
On the negative side, a consistent choice of local spanning tree data does
depend on choosing a monomial order. This order is nowhere explicit, but
with
some orders the choices made in educational examples fail. Who can
guarantee
that the same will never happen in future real world examples, unless we
make
the implicit order explicit?
On the neutral side, I am still not sure whether my consistency test is
airtight and waterproof...
--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:436>
Sage <http://www.sagemath.org>
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