#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 vbraun):
Replying to [comment:485 nthiery]:
> What I meant however is that, at the level of categories, the
> "super-category" relation should not be modeled by inheritance.
Must not, should not, need not? I agree, of course, that the category-
relationship is unrelated to the object-relationship. But if its
convenient to define your category by object-inheriting from another
category, then why not?
I would prefer to treat axioms as independent from categories (i.e. they
don't inherit from Category). That then also gives you a non-category
object that you can use to represent the axiom. Now, since you always have
to create (manually or dynamically) a new class for a category-with-axiom
it might just as well inherit from the axiom class(es). Though if you
think its confusing then I'm also open to using a special class attribute
and composition.
Now for something different. For the super categories, is the following
what we really want? Its good enough for figuring out the methods, but
does contradict the `super_category` documentation:
{{{#!python
class Base(Category_singleton):
def super_categories(self):
return [Objects()]
class SubcategoryMethods:
A = axiom("A")
B = axiom("B")
C = axiom("C")
class A(CategoryWithAxiom):
pass
class B(CategoryWithAxiom):
pass
class C(CategoryWithAxiom):
pass
Base().A() in Base.A().B().C().super_categories() # True, even
though not direct supercategory
Base().A().B() in Base.A().B().C().super_categories() # False
Base().A().B() in Base.A().B().C().all_super_categories() # False
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:486>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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