#16340: Infrastructure for modelling full subcategories
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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|
d4c7a88563a397291b6cd5ddadb8f574cc1eedb5
Dependencies: | Stopgaps:
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Comment (by tscrim):
Replying to [comment:41 pbruin]:
> What is a functorial construction category? From the documentation it
appears that the idea is that one first defines a construction in some
"abstract" sense, and only then decides in which category it takes its
values, or even to construct a completely new category for this. I
realise that the code doesn't have to follow mathematical definitions
exactly, but this seems to be quite the opposite of the usual pattern of
doing things, where defining a function, functor or natural transformation
presupposes that a domain and codomain have been fixed. In general this
is essential because the function (etc.) that one defines, and its
properties, depend on these choices. I am somewhat worried that the Sage
implementation might rely (maybe just in subtle ways) on the intuition
behind the cases where this advance choice of domain and codomain doesn't
matter so much.
The examples are graded modules/algebras and `WithRealizations`. From
those examples, I would say the categories that are actually used have a
fixed (co)domain. I also think this is similar to morphisms, which also
makes the assumption of a fixed (co)domain, but perhaps things are
different in this case? I'm not sure I understand your concern here...
--
Ticket URL: <http://trac.sagemath.org/ticket/16340#comment:42>
Sage <http://www.sagemath.org>
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