I am playing with an experimental implementation of "enumerated" axiom. The
results are interesting.
sage -t src/sage/combinat/posets/posets.py
**********************************************************************
File "src/sage/combinat/posets/posets.py", line 755, in
sage.combinat.posets.posets.FinitePoset
Failed example:
P.category()
Expected:
Join of Category of finite posets and Category of finite enumerated sets
Got:
Category of finite enumerated posets
**********************************************************************
File "src/sage/combinat/posets/posets.py", line 776, in
sage.combinat.posets.posets.FinitePoset
Failed example:
P.category()
Expected:
Join of Category of finite posets and Category of finite enumerated sets
Got:
Category of finite enumerated posets
**********************************************************************
File "src/sage/combinat/posets/posets.py", line 782, in
sage.combinat.posets.posets.FinitePoset
Failed example:
Q.category()
Expected:
Join of Category of finite posets
and Category of finite enumerated sets
and Category of facade sets
Got:
Category of facade finite enumerated posets
**********************************************************************
File "src/sage/combinat/posets/posets.py", line 793, in
sage.combinat.posets.posets.FinitePoset
Failed example:
PQ.category()
Expected:
Join of Category of finite posets
and Category of finite enumerated sets
and Category of facade sets
Got:
Category of facade finite enumerated posets
**********************************************************************
File "src/sage/combinat/posets/posets.py", line 805, in
sage.combinat.posets.posets.FinitePoset
Failed example:
QP.category()
Expected:
Join of Category of finite posets
and Category of finite enumerated sets
Got:
Category of finite enumerated posets
These seem rather nice :-) On the other hand,
sage -t src/sage/categories/division_rings.py
**********************************************************************
File "src/sage/categories/division_rings.py", line 81, in
sage.categories.division_rings.DivisionRings.Finite_extra_super_categories
Failed example:
DivisionRings().Finite()
Expected:
Category of finite fields
Got:
Category of finite enumerated fields
This is rather ugly. I guess that this is caused partially by that the
"finite" axiom does not imply "enumerated" axiom, which is legitimate. Do
you think "enumerated" axiom should be in Sage or not?
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