#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,     |  ec340363a811bbafbb8cd5ff8f39e75db9872f9f
  #10193, #12895, #14516, #14722,    |     Stopgaps:
  #13589, #14471, #15069, #15094,    |
  #11688, #13394, #15150, #15506     |
-------------------------------------+-------------------------------------

Comment (by SimonKing):

 Aha, it is not so easy. It turns out that the lazy attribute is involved
 much more often, but not during startup of Sage.

 For example, when you start Sage, then `FinitePermutationGroups` are not
 constructed by means of applying an axiom. Hence, the attribute is not
 available. Hence, things crash.
 {{{
 sage: FinitePermutationGroups()
 # Note: Here I have replaced the lazy axiom by something that just raises
 an error
 Traceback (most recent call last):
 ...
 AttributeError: <class
 'sage.categories.finite_permutation_groups.FinitePermutationGroups'> does
 not know its base category and axiom
 }}}
 If one then constructs the category ''class'' (not instance!) by means of
 an axiom, thing work:
 {{{
 sage: PermutationGroups.Finite
 <class
 'sage.categories.finite_permutation_groups.FinitePermutationGroups'>
 sage: FinitePermutationGroups()
 Category of finite permutation groups
 }}}

 So, it seems that we have to live with the guesswork. But I wonder if we
 can simplify the logic, and can make it so that categories with axiom can
 be defined interactively.

--
Ticket URL: <http://trac.sagemath.org/ticket/10963#comment:309>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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