#10667: Morphisms and Objects of Categories
---------------------------+------------------------------------------------
Reporter: SimonKing | Owner: nthiery
Type: enhancement | Status: new
Priority: major | Milestone:
Component: categories | Keywords: objects morphisms containment
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
---------------------------+------------------------------------------------
'''__Purpose__'''
Introduce a framework for testing whether or not something is a morphism
in a category. See the discussion on [http://groups.google.com/group/sage-
algebra/browse_thread/thread/3e2ca2a8be1a3a23 sage-algebra]. Here is a
summary of the discussion.
__Methods for categories__
Categories `C` should have a method `C.has_morphism(f)` answering whether
`f` is a morphism in `C`. By symmetry, we want a method `C.has_object(X)`,
answering whether `X` is an object in `C`.
Note that we want `X in C` to be true if and only if `X` is an object of
`C` (so, it is synonymous to `C.has_object(X)`). This currently is not
always the case:
{{{
sage: P.<x,y> = QQ[]
sage: f = P.hom(reversed(P.gens()))
sage: f in Rings().hom_category()
True
}}}
but of course `f` is not an ''object'' of the hom-category (it is only
''contained'' in an object of the hom-category).
__Class/Set of objects and morphisms__
It would be nice to have container classes for the objects and for the
morphisms of a category. Then, `f in C.morphisms()` would be a very
natural notation for `C.has_morphism(f)`, and `X in C.objects()` would be
another way of saying `X in C`.
Of course, since `f in C.morphisms()` and `f in C.objects()` are nice
notations, they should be as fast as possible -- otherwise, people
wouldn't use them.
Further discussion should be put in comments to this ticket.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10667>
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 post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
