#19397: Add support for homogeneous components of a filtered module
-------------------------------------+-------------------------------------
       Reporter:  tscrim             |        Owner:  sage-combinat
           Type:  enhancement        |       Status:  needs_work
       Priority:  major              |    Milestone:  sage-6.10
      Component:  categories         |   Resolution:
       Keywords:                     |    Merged in:
        Authors:  Travis Scrimshaw   |    Reviewers:  John Palmieri
Report Upstream:  N/A                |  Work issues:
         Branch:                     |       Commit:
  public/categories/homogeneous_components-19397|  
f89275b059b5dee1488feee46090596c157615c0
   Dependencies:  #17096             |     Stopgaps:
-------------------------------------+-------------------------------------
Changes (by tscrim):

 * cc: SimonKing (added)


Comment:

 I can also reproduce this by just running the tests on
 `modules_with_basis.py`.

 I tried the same hack on #15536 and I got errors. To the extreme, I made
 the prime check on the input for `Zmod` and removed the category
 refinement, and I ''still'' got errors.

 I am strongly inclined to believe that it is not an issue with category
 refinement, but instead something is wrong with how the category MRO is
 being constructed. I would want to simultaneously fix for both #15536 and
 this, but I'm fairly convinced they are different issues.

 Yet another data point. I created a separate class and file for the new
 category, and then set `FiniteDimensionalModulesWithBasis.Filtered` to
 this new class (also now inheriting from `FilteredModulesCategory` by
 following what `GradedHopfAlgebrasWithBasis` does). This now does not set
 the correct category as
 {{{
 sage: (ModulesWithBasis(ZZ).Filtered().FiniteDimesnional()
 ....:  != ModulesWithBasis(ZZ).FiniteDimesnional().Filtered())
 False
 }}}
 This is on `u/tscrim/test-19397`.

 I have absolutely no idea what is going on. I would appreciate some
 comments from those that implemented how the category code handles these
 things.

--
Ticket URL: <http://trac.sagemath.org/ticket/19397#comment:20>
Sage <http://www.sagemath.org>
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