#16340: Infrastructure for modelling full subcategories
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Reporter: nthiery | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: categories | Resolution:
Keywords: full | Merged in:
subcategories, homset | Reviewers: Darij Grinberg,
Authors: Nicolas M. Thiéry | Travis Scrimshaw, Simon King
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/categories/full_subcategories-16340|
eb621c7beacb797f43fd41c9156edc453e80a902
Dependencies: | Stopgaps:
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Comment (by SimonKing):
Replying to [comment:53 tscrim]:
> Replying to [comment:52 pbruin]:
> > It may be because I'm still misled by the terminology, but I'm afraid
this only increases my confusion about what functorial construction
categories are. In what sense do "topological" and "metric" have
something to do with modelling codomains of a collection of functors? (Of
course topological/metric spaces can be domains/codomains of functors, but
I don't think this is what Nicolas meant in comment:49).
> >
> > To me "topological" and "metric" are examples of "extra structure", in
the sense that there are canonical functors (metric spaces) ->
(topological spaces) -> (sets). In the current Sage
implementation/parlance, I guess they would be regarded as examples of
axioms.
>
> This may not be the right way, but I think of these functional
construction categories as additional data to some base category `C` in
which every object of `C` has a natural way to construct this data that
preserves the morphisms. For graded, make everything be in the 0-th graded
part. For metric/topological, give it the discrete metric/topology.
>
> Actually running with that example, an object in graded algebras would
be the pair `(A, deg)`, right? So if we consider the section of the
forgetful function where `deg(x) = 0` for all `x` in `A`, this would have
algebras as a full subcategory of graded algebras, right? So I think we
might need to be careful with how we are considering the base categories
inside of the functorial construction category. On that, I reverse my
position, functorial construction categories should not be structure
categories because of the natural inclusion mentioned above (unless I'm
wrong).
I am not very much confident about the functorial constructions either. I
am (re-)reading the chapter on functorial constructions in the category
primer right now.
Anyway, it seems to me that Nicolas has addressed the concerns expressed
here (I was rereading all comments), the code is relatively clear (to me,
the unclear parts concern things that existed before, like functorial
constructions), and moreover all tests pass. So, if nobody objects, I am
putting this to positive review, after reading the chapter in the
primer...
--
Ticket URL: <http://trac.sagemath.org/ticket/16340#comment:61>
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