#10963: More functorial constructions
-------------------------------------+-------------------------------------
       Reporter:  nthiery            |        Owner:  stumpc5
           Type:  enhancement        |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-6.1
      Component:  categories         |   Resolution:
       Keywords:  days54             |    Merged in:
        Authors:  Nicolas M. Thiéry  |    Reviewers:  Simon King, Frédéric
Report Upstream:  N/A                |  Chapoton
         Branch:                     |  Work issues:
  public/ticket/10963                |       Commit:
   Dependencies:  #11224, #8327,     |  8045aa4a4b7ada735b3eb6055382f9b341a39f1e
  #10193, #12895, #14516, #14722,    |     Stopgaps:
  #13589, #14471, #15069, #15094,    |
  #11688, #13394, #15150, #15506     |
-------------------------------------+-------------------------------------

Comment (by vbraun):

 I agree with Nils, but imho that is just another way of spelling out the
 problem. What does adding the ''Finite'' axiom actually mean if I want to
 apply it to a category that I'm using/writing?  I can guess that it gives
 me a `is_finite()` method returning `True`, but confusingly that is
 implemented in some category. Anything else? How can I use code
 introspection (one of Pythons absolute strong points) to find out what is
 going on? I can't, because all I got is this string to represent the
 axiom. Axioms should be **code** (classes) with some protocol for how they
 are used to enrich categories.

 Slightly related, I don't like the `_base_category_class_and_axiom`
 attribute. A heterogeneous list with some convention to treat the first
 element special is a terrible data structure. Just split it up into
 `_base_category_class` and `_axioms`.

--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:383>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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