#18175: Implement categories for topological and metric spaces and related
categories
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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):
Hey Basile,
I'm not quite sure what you're proposing we should do for organizing the
manifolds category. For the (a) <=> (b) condition, we aren't doing any
sort of checking. By a user constructing a object (parent) in a category,
the user is simply promising that it carries that structure.
We could make it so there is no parameterization of the categories (on the
underlying field), but instead have the condition for objects to be in the
category that their base field be '''R''' or '''C''' as appropriate.
However I think this leads to ambiguity of dimension (e.g., for complex
manifolds, do you want the real or complex dimension?) and what you want
your charts to be.
I think for fields like '''Q''', the metric gives a good notation of
convergence, limits, and hence differential calculus. So, e.g., for smooth
manifolds, the transition maps would still be smooth maps (just now in
terms of '''Q''' calculus instead of '''R''' calculus).
Are you perhaps suggesting we should do something like the digram in
comment:21?
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Ticket URL: <http://trac.sagemath.org/ticket/18175#comment:25>
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