#19269: add category Posets to ZZ and QQ
-------------------------------------+-------------------------------------
Reporter: dkrenn | Owner:
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-6.9
Component: categories | Resolution:
Keywords: | Merged in:
Authors: Daniel Krenn | Reviewers:
Report Upstream: N/A | Work issues:
Branch: u/dkrenn/cat/ZZ- | Commit:
poset | c1d0720cc0b80041c8fdda8c85ec89bc031749ae
Dependencies: | Stopgaps:
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Comment (by vdelecroix):
Replying to [comment:12 dkrenn]:
> Replying to [comment:6 vdelecroix]:
> > Having so many category for `ZZ` might also be a problem when it comes
to morphisms. What should be
> > {{{
> > sage: Hom(ZZ,ZZ)
> > sage: Hom(ZZ^2, ZZ^2)
> > }}}
> > In the category of `Euclidean domains + Posets` there are few
elements! And most of the time, when people think about `ZZ^2` they do not
care about the poset structure. Something likethe following should work
out of the box
> > {{{
> > sage: Hom(ZZ^2, ZZ^2, Posets())
> > sage: Hom(ZZ^2, ZZ^2, Modules(ZZ))
> > }}}
> > My question is about the default behavior of `Hom` with this multiple
categories.
>
> What would be a solution to this or what are possible scenarios? What
can we do to get this ticket (make ZZ and QQ posets) towards a positive
review?
Indeed, it was a question... One possibility: make some priorities for the
`Hom` functor in `sage.categories.homset`.
Currently, to deduce the category of `Hom(X,Y)` the functor does
`X.category()._meet_(Y.category())` which is documented as being "the
largest common subcategory of self and other". Instead of `_meet_` one
could try to implement a more dedicated method that forget some of the
categories (such as the Poset one if there is some algebraic structure).
Vincent
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Ticket URL: <http://trac.sagemath.org/ticket/19269#comment:13>
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