#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 pbruin):
Replying to [comment:48 nthiery]:
> Time for a checkpoint on the current status.
>
> == Permutation groups ==
>
> Looking back at Travis change, I would want to also revert the change
> to `PermutationGroups()`, to let it be a structure category. Indeed,
> permutation groups come with a distinguished action, and Wikipedia
> states that this action should be preserved by isomorphisms:
>
>
http://en.wikipedia.org/wiki/Permutation_group#Permutation_isomorphic_groups
>
> Do you agree?
Yes, the set that is acted upon does seem to qualify as extra structure.
> == additional_structure w.r.t. full_super_categories ==
>
> As discussed above, I believe that having the developer implement
> `additional_structure` rather than `full_super_categories` is more
> concise and involves less duplication. And also gives more information
> (which category define additional structure) which could be further
> refined (e.g. "Magmas()" defines "*"), if deemed useful in later
> iterations.
>
> Is this acceptable for everyone?
That sounds good to me.
> == additional_structure w.r.t is_structure_category ==
>
> Do we have a consensus that the "additional_structure / structure"
> language is better than "is_structure_category /
> all_structure_super_categories"? And that for now we can specify that
> `C.additional_structure()` shall return `C` or `None`?
>
> If yes, I can implement this change shortly.
I am in favour of this change.
> == Default for axioms ==
>
> Currently, axiom categories define no additional structure by default.
> To be 100% foolproof even when defining new axioms, one could change
> that so an axiom category `C().A()` would by default define additional
> structure if and only if `C` is the category defining the axiom `A`.
I am not in favour of this, because it would conflate the notions of
"axiom" and "extra structure" (which from my perspective are quite
different) even more.
--
Ticket URL: <http://trac.sagemath.org/ticket/16340#comment:51>
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.
