#12876: Fix element and parent classes of Hom categories to be abstract, and
simplify the Hom logic.
----------------------------------------------------------------+-----------
       Reporter:  nthiery                                       |         
Owner:  nthiery     
           Type:  enhancement                                   |        
Status:  needs_review
       Priority:  major                                         |     
Milestone:  sage-pending
      Component:  categories                                    |    
Resolution:              
       Keywords:  categories, Hom                               |   Work 
issues:              
Report Upstream:  N/A                                           |     
Reviewers:  Simon King  
        Authors:  Nicolas M. ThiƩry                             |     Merged 
in:              
   Dependencies:  #715, #11521, #12215, #12313, #13412. #13145  |      
Stopgaps:              
----------------------------------------------------------------+-----------
Changes (by nthiery):

  * status:  needs_work => needs_review
  * work_issues:  failing tests; design issue =>


Comment:

 Two failures were actually trivial:

 - A trivial doctest in
   devel/sage/doc/en/thematic_tutorials/coercion_and_categories.rst
 - More skips were needed in the new TestSuite(H) in line 114 of
 sage.categories.hecke_modules
   (some new test methods that require the currently missing an_element
 were added since last year)

 I implemented a simplistic protocol for the above issue. If P._Hom_ fails,
 then try category.parent_class._Hom_. This is sufficient for the other
 failing test in Parent.

 Other than this, the attached patch is a straightforward rebase of the
 previous one. So to finalize the review it would suffice to:

 - glance at the above change
 - recheck sage.categories.homset.Hom

 I am currently running the long tests, but I expect everything to pass.

 Almost done!

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12876#comment:107>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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