#10963: More functorial constructions
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Reporter: nthiery |
Owner: stumpc5
Type: enhancement |
Status: needs_review
Priority: major |
Milestone:
Component: categories |
Resolution:
Keywords: |
Work issues: Rebase wrt. #13589
Report Upstream: N/A |
Reviewers: Simon King
Authors: Nicolas M. Thiéry |
Merged in:
Dependencies: #11224, #8327, #10193, #12895, #14516, #14722, #13589 |
Stopgaps:
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Comment (by nthiery):
Replying to [comment:25 SimonKing]:
> Yes. A not necessarily unital not necessarily associative not
> necessarily finite-dimensional not necessarily noetherian not
> necessarily ... is commonly known as an '''algebra'''.
Yup, and that's indeed what Wikipedia says which is a good
point. However in many textbooks and other pieces of literature
"algebra" implicitly includes "associative" and "unital" (for the same
reason that it will be heavy for us to write almost everywhere
Algebras().Associative().Unital()).
More importantly: changing the semantic current "Algebras" in Sage
would be seriously backward incompatible. And we would have to think
about what we want to do about categories like "HopfAlgebras" to keep
things consistent.
So I definitely see your point but at this point I am not keen on
opening yet another can of worms (both technical and social) to this
already too big patch.
> Actually, before reading your patch, I thought that you aim to
> ''automatically'' create a category of "associative algebras",
> given the category of algebras and the axiom "associative".
Up to the names, that's precisely what's its doing :-)
> Hence, I think it should be
{{{
algebras
/ \
associative algebras unital algebras
\ /
associative unital algebras
}}}
What about, at least as a temporary measure, going for:
{{{
magmatic algebras
/ \
associative magmatic algebras unital magmatic algebras
\ /
algebras
}}}
(or any other not-yet-used name you like instead of "magmatic
algebra")
Cheers,
Nicolas
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10963#comment:26>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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