On Friday, June 15, 2018 at 2:36:55 AM UTC-7, Travis Scrimshaw wrote:
>
> Hey John,
>
> Okay, so how do I define a new category in Sage? There is some magic
>> happening somewhere in the category stuff, and I don't know where it's
>> documented.
>>
>
>> I am in particular interested in creating two categories:
>>
>> - GradedCommutativeAlgebras
>> - GradedCommutativeAlgebrasWithBasis
>>
>> (and then perhaps similarly for coalgebras and Hopf algebras).
>>
>
> Yes, there is some magic going on in order to remove some boilerplate type
> stuff (in this case, defining the base category). In part, because you are
> doing a functorial construction, things are a little more complicated.
> Actually, you will probably want to use the super modules/algebras as your
> reference, maybe even as your base category. This probably has some of the
> functionality you want and supercommutative algebras will benefit as well.
>
> Another question: is the categories primer still accurate? It says (
>> http://doc.sagemath.org/html/en/reference/categories/sage/categories/primer.html#writing-a-new-category
>>
>> <http://www.google.com/url?q=http%3A%2F%2Fdoc.sagemath.org%2Fhtml%2Fen%2Freference%2Fcategories%2Fsage%2Fcategories%2Fprimer.html%23writing-a-new-category&sa=D&sntz=1&usg=AFQjCNGnvXjlXmpV-Jc6ufZDEsGYPrPTxw>)
>>
>> that when defining new categories, you have to provide a method
>> C.super_categories(), but many constructions in the categories directory
>> (like graded_algebras_with_basis.py) do not explicitly do this.
>>
>
> Yes, it is still implicitly accurate, but the necessity is only about
> constructing a simple category. If you use an axiom or functorial
> construction, then these provide a generic super_categories() by magic.
>
> Best,
> Travis
>
>
That leads me (or brings me back) to these questions: what is the magic
that is going on, is it documented, and if so, where? If not, there must be
a ticket for writing category documentation, right?
If I look at super_algebras.py, for example, I see
class SuperAlgebras(SuperModulesCategory):
and not much else. I don't see a lot more in
super_modules.SuperModulesCategory. How is this "doing a functorial
construction," as you put it?
--
John
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