#10667: Morphisms and Objects of Categories
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Reporter: SimonKing | Owner: nthiery
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-5.0
Component: categories | Keywords: objects morphisms
containment
Work_issues: Cartesian products | Upstream: N/A
Reviewer: | Author: Simon King
Merged: | Dependencies: #9138, #11115, #11780
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Comment(by nthiery):
Replying to [comment:43 SimonKing]:
> Just a status report: I got rid of the `__new__` method. Instead, I
produce a `__classcall__` method,
Sounds good. I guess I had not yet implemented __classcall__ when I
wrote the __new__ workarounds.
> similar to what is done in `UniqueRepresentation` (and in fact I make
`sage.categories.rings.Rings.HomCategory.ParentClass` inherit from
`UniqueRepresentation`).
I am not absolutely sure about this: as for parents, it is recommended
for Homsets to have unique representation, but I am not sure this is
currently *required* and *enforced*. So this may open a larger can of
worm than this ticket can handle. This might be the issue you
encountered with polynomials.
> After my patches and the addition of the base_ring method to Cartesian
product categories, the problem arose with `__init_extra__` method in
`sage.categories.algebras.Algebras.ParentMethods`: The Cartesian product
of algebras over a ring R is an algebra over R (apparently acting
diagonally). The `__init_extra__` tries to create a coercion from the R to
the cartesian product. However, that ended in an infinite recursion. I
solved it by adding a `from_base_ring` method, that is understood by
`__init_extra__`.
Cool!
> The remaining problem concerns summation of elements of Cartesian
products. Multiplication is defined, via
`sage.categories.magmas.Magmas.CartesianProduct.ParentMethods.product`.
But summation is missing. I guess it should be implemented in
`sage.categories.AdditiveMagmas.CartesianProduct.ParentMethods.summation`.
Thanks for implementing this missing piece!
Cheers,
Nicolas
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10667#comment:50>
Sage <http://www.sagemath.org>
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