#16340: Infrastructure for modelling full subcategories
-------------------------------------+-------------------------------------
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
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/categories/full_subcategories-16340|
60aa128d42ee140fb268423a924fd0e80aab7329
Dependencies: | Stopgaps:
-------------------------------------+-------------------------------------
Comment (by 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).
--
Ticket URL: <http://trac.sagemath.org/ticket/16340#comment:53>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
