#10963: Axioms and more functorial constructions
-------------------------------------+-------------------------------------
       Reporter:  nthiery            |        Owner:  stumpc5
           Type:  enhancement        |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-6.2
      Component:  categories         |   Resolution:
       Keywords:  days54             |    Merged in:
        Authors:  Nicolas M. Thiéry  |    Reviewers:  Simon King, Frédéric
Report Upstream:  N/A                |  Chapoton
         Branch:                     |  Work issues:  To be merged
  public/ticket/10963-doc-           |  simultaneously with #15801
  distributive                       |       Commit:
   Dependencies:  #11224, #8327,     |  96fa89eaefdbb020d748e42ab23b9a7545621a14
  #10193, #12895, #14516, #14722,    |     Stopgaps:
  #13589, #14471, #15069, #15094,    |
  #11688, #13394, #15150, #15506,    |
  #15757, #15759, #16244             |
-------------------------------------+-------------------------------------

Comment (by SimonKing):

 The element methods of Algebras(...) used to provide a copy of
 `sage.structure.element.AlgebraElement.__mul__` (implementing the coercion
 framework), but now it is gone. Is this a wise decision? Generally I'd say
 that one ''should'' start with `sage.structure.element.AlgebraElement`
 when one is implementing elements of an algebra.

 However, because of subtle bug in Cython, it is I think possible to create
 a Python class inheriting from `sage.categories.map.Map` and
 `sage.structure.element.AlgebraElement`, but then certain cdef attributes
 of the two base classes will be confused (hence, the two base classes are
 actually incompatible, but Cython does not notice).

 Hence, there will be cases (such as endomorphism rings) where one has an
 algebra formed by maps, and one can not use
 `sage.structure.element.AlgebraElement` as a base class. It would then be
 very handy if one could inherit coercion from the category's
 element_class.

--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:733>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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