#18175: Implement categories for topological and metric spaces and related
categories
-------------------------------------+-------------------------------------
Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.8
Component: categories | Resolution:
Keywords: geometry, | Merged in:
topology, sd67 | Reviewers:
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 95a30aa57fc62f23a884790b57835d107d8bdeef
public/categories/topological_metric_spaces-18175| Stopgaps:
Dependencies: #18174 #17160 |
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Comment (by tscrim):
It still seems like we are having an assumption that all manifolds can
inherently be realized over '''R'''. This was my initial assumption too,
and so manifolds that could be locally homoemorphic to '''C'''^d^ were a
special case.
However I feel like it would be best for `Manifolds` to be over an
arbitrary topological field (which will require some very mild changes).
So then the heirarchy for manifolds then be:
{{{
Manifolds
|
Differentiable
|
Smooth
/ \
Analytic AlmostComplex
|
Complex
}}}
Do we think we should add a stub category for PL and/or (pseudo)
Riemannian manifolds? How about `ManifoldsWithBoundary` as a supercategory
of `Manifolds` (and how many of these extra structures lift to the
boundary)?
A question for CW complexes, should the elements of a CW complex be the
cells or the points of the topological space? Right now, I'm taking the
former approach, but I feel this might be an abuse as these should be
subobjects of the category (Nicolas, any wisdom to impart on this?). If
this seems like a non-trivial issue, I can split this ticket into 2 parts;
one for the manifolds and one for the CW complexes.
--
Ticket URL: <http://trac.sagemath.org/ticket/18175#comment:20>
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