Category Modules ~> Algebras

[sagetrac-elixyre]

Strange problem:

from sage.categories.category_types import Category_over_base_ring

class A(Category_over_base_ring):
    
    def super_categories(self):
        R = self.base_ring()
        return [Algebras(R]
        #return [Modules(R)]
    
class B(UniqueRepresentation, Parent):
    
    def __init__(self, R):
        Parent.__init__(self, category=A(R))

That fails! (6.2 rc 2):

sage: B(QQ)
...
TypeError: None is not in Category of rings

But if I try to change the super categories:

Algebras(R) --> Modules(R)

That works! What's error mean?

CC: @nthiery

Component: categories

Issue created by migration from https://trac.sagemath.org/ticket/16443

[nthiery]

comment:1

It in fact does not work either: a parent in Modules(...) should
implement a base_ring method. This method just turns out not to be
called upon initialization if B is just in Modules() instead of
Algebras(), so the problem goes undetected, so far ...

It indeed feels a bit redundant to have to specify the base ring in
the category and in the base_ring method. The thing is that, in the
category, one can now specify something like Algebras(Rings()); I'd
say it's even recommended. So one can't recover the base ring from the
just the category. It's not so bad, because more often than not, when
implementing a module, one inherits from some preexisting module that
implements base_ring for us.

Now, yes, definitely, this all might not be stated explicitly in the
documentation; and the error message is not informative ...

Step that can be taken right away:

• add a base_ring abstract method in Modules.ParentMethods

Steps that are a bit more tricky (I tried and dropped the case; but I
had to act fast then to get #10963 in):

• Remove the base_ring method from CategoryObject (it has nothing to
  do there).

• Implement a base_ring method for all the existing modules
  (polynomials, ...), putting it in common abstract super classes
  whenever possible.

Cheers,
Nicolas