#18309: Categories are wrong for Hom/cartesian products of vector spaces
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   Reporter:  vdelecroix  |            Owner:
       Type:  defect      |           Status:  new
   Priority:  major       |        Milestone:  sage-6.7
  Component:  categories  |         Keywords:
  Merged in:              |          Authors:
  Reviewers:              |  Report Upstream:  N/A
Work issues:              |           Branch:
     Commit:              |     Dependencies:
   Stopgaps:              |
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 {{{
 sage: cartesian_product([GF(3)^2, GF(7)^3])
 The cartesian product of (
   Vector space of dimension 2 over Finite Field of size 3,
   Vector space of dimension 3 over Finite Field of size 7)
 sage: _.category()
 Category of Cartesian products of vector spaces with basis over
  (finite fields and subquotients of monoids and quotients of semigroups)
 }}}
 and
 {{{
 sage: Hom(GF(3)^2, GF(7)^3)
 Set of Morphisms (Linear Transformations) from
   Vector space of dimension 2 over Finite Field of size 3
 to
   Vector space of dimension 3 over Finite Field of size 7
 sage: _.category()
 Category of homsets of modules with basis over
  (finite fields and subquotients of monoids and quotients of semigroups)
 }}}

 see also: #16940

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Ticket URL: <http://trac.sagemath.org/ticket/18309>
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