#16340: Infrastructure for modelling full subcategories
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Reporter: nthiery | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.3
Component: categories | Resolution:
Keywords: full | Merged in:
subcategories, homset | Reviewers:
Authors: Nicolas M. Thiéry | Work issues:
Report Upstream: N/A | Commit:
Branch: | 2f2d09bec3a2e77021670d996abe2dd399fc63ec
u/nthiery/categories/full- | Stopgaps:
subcategories-16340 |
Dependencies: |
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Comment (by nthiery):
One thing I don't know how to handle. Assume we want the morphisms of
euclidean rings to preserve euclidean division (I'd say that this is
equivalent to preserving the degree). Then, `EuclideanDomains()` is not a
full subcategory of `Rings()`. Yet `Fields()`, which is a subcategory of
`EuclideanDomains()`, is a full subcategory of `Rings()`. This is because
the additional structure defined by `EuclideanDomains()` (the degree) is
trivial in this case.
We can't model this in the current implementation. An approach might be to
have `Fields()` explicitly remove `EuclideanDomains()` from its structure
categories. But then we have to be more careful in the full subcategory
test. Maybe we can test, for B a subcategory of A that
`B.super_structure_categories()` is a subset of
`A.super_structure_categories()`; given that we hash and check for
equality by id, that should be fast enough if deemed correct.
A similar situation appears for graded connected hopf algebras where there
is a single choice for the antipode (and, IIRC, it's preserved for free by
bialgebra morphisms). So this is a full subcategory of the category of
bialgebras.
Cheers,
Nicolas
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Ticket URL: <http://trac.sagemath.org/ticket/16340#comment:13>
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