#8881: Functorial constructions in categories
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   Reporter:  hivert             |       Owner:  nthiery                 
       Type:  enhancement        |      Status:  needs_review            
   Priority:  major              |   Milestone:  sage-4.4.3              
  Component:  categories         |    Keywords:  Functorial constructions
     Author:  Nicolas M. ThiƩry  |    Upstream:  N/A                     
   Reviewer:  Florent Hivert     |      Merged:                          
Work_issues:                     |  
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Changes (by nthiery):

 * cc: sage-combinat (added)
  * keywords:  Functorial construction => Functorial constructions


Old description:

> Add functorial construction to categories. Examples include
>    Tensor products, Group/Monoids/*Algebras, Subquotient...

New description:

 This patch refactors completely the framework for (covariant)
 functorial constructions, improves the existing ones, and adds new ones.

 Improved constructions:
  - Cartesian products: generalization to non modules_with_basis,
    monoid operations, ...

 New constructions:
  - Subquotients, Quotients, Subobjects, IsomorphicObjects
  - DualObjects, Algebras

 Miscellaneous category fixes and improvements:
  - is_subcategory now handles properly join categories
    (courtesy of Florent Hivert)
  - For a field K, Modules(K) returns VectorSpaces(K)
  - As a temporary workaround, Parent._an_element_ calls the
    _an_element_ method provided by the categories, if available
  - Adds a method Category.or_subcategory
  - Cleans up _repr_ by extracting a _repr_object_names method
  - Cleans up _latex_ by extracting a _short_name method

--

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8881#comment:2>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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