wiki:CategoriesCategoriesReview

Version 42 (modified by kohel, 5 years ago) (diff)

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Splitting of the review of the categories


Franco Saliola:

semigroups                       (positive review)
examples/semigroups              (positive review)
examples/semigroups_cythonx      (Florent - positive review - as a proof of concept)
monoids                          (positive review)
examples/monoids                 (positive review)
examples/finite_semigroups       (positive review)
finite_semigroups                (positive review)
finite_monoids                           (Florent - positive review)
examples/finite_monoids                  (Florent - positive review)
commutative_additive_semigroups          (Florent - positive review)
examples/commutative_additive_semigroups (Florent - positive review)
commutative_additive_monoids             (Florent - positive review)
examples/commutative_additive_monoids    (Florent - positive review)
commutative_additive_groups              (Florent - positive review)

Nicolas (code by Florent)

examples/sets_cat                 (positive review)

enumerated_sets                   (positive review)
finite_enumerated_sets            (positive review)
examples/finite_enumerated_sets   (positive review)
infinite_enumerated_sets          (positive review)
examples/infinite_enumerated_sets (positive review)

Jason Bandlow:

modules_with_basis                (positive review)

Florent:

sets_cat                                    (positive review)
algebras                                    (positive review - Anne)
algebras_with_basis                         (positive review)
examples/algebras_with_basis                (positive review)

hopf_algebras                               (positive review)
hopf_algebras_with_basis                    (positive review)
examples/hopf_algebras_with_basis           (positive review)

coalgebras                                  (positive review)
coalgebras_with_basis                       (positive review)

bialgebras                                  (positive review -- Essentially empty)
bialgebras_with_basis                       (positive review -- Essentially empty)

finite_dimensional_algebras_with_basis      (positive review)
finite_dimensional_bialgebras_with_basis    (positive review -- Essentially empty)
finite_dimensional_coalgebras_with_basis    (positive review -- Essentially empty)
finite_dimensional_hopf_algebras_with_basis (positive review -- Essentially empty)
finite_dimensional_modules_with_basis       (positive review -- Essentially empty)

graded_algebras                             (positive review -- Essentially empty)
graded_algebras_with_basis                  (positive review -- Essentially empty)
graded_bialgebras                           (positive review -- Essentially empty)
graded_bialgebras_with_basis                (positive review -- Essentially empty)
graded_coalgebras                           (positive review -- Essentially empty)
graded_coalgebras_with_basis                (positive review -- Essentially empty)
graded_hopf_algebras                        (positive review -- Essentially empty)
graded_hopf_algebras_with_basis             (positive review)
graded_modules                              (positive review -- Essentially empty)
graded_modules_with_basis                   (positive review -- Essentially empty)

group_algebras                              (Positive review -- Essentially empty)

Florent: The two following aim to define operads over some ring. I marked them to be discussed since they are essentially empty and that if we want to have operads say in the category of sets then we will run into trouble with the naming convention... The proper setting would maybe to define operads as functorial constructions like tensor product...

Nicolas: Ok. Those were just the straightforward translations of the corresponding categories in MuPAD-Combinat, but indeed the new framework may allow for a better design. I'll split them out in a separate patch, and we will see in the future what we will do with them when we will have concrete examples.

operads                       (100% doctest)     (postponed for later)
operads_with_basis            (100% doctest)     (postponed for later)

David Kohel, Javier, or whoever wants to take some of those.

Note: there are lots of them, but they are all essentially empty and already 100% doctested, so the review should be super quick.

all                            (100% doctest)
basic                          (100% doctest)

algebra_ideals                 (positive review - Javier)
algebra_modules                (100% doctest - Javier)
bimodules                      (positive review - Javier)
commutative_algebra_ideals     (positive review - Javier)
commutative_algebras           (positive review - Javier)
commutative_ring_ideals        (positive review - Javier)
commutative_rings              (positive review - Javier)
division_rings                 (positive review - Javier)
entire_rings                   (100% doctest - Javier)
euclidean_domains              (positive review - Javier)
fields                         (positive review - David K)
finite_fields                  (positive review - David K)
g_sets                         (positive review - Florent)
gcd_domains                    (positive review - Javier)
groupoid                       (positive prereview - Florent; please someone double check)
hecke_modules                  (positive review - David K: this should probably be revisited -- notes a hecke algebra or ring category to be useful; this is probably not currently used.)
integral_domains               (positive review - Javier)
left_modules                   (100% doctest - Javier)
matrix_algebras                (positive review - David K)
modular_abelian_varieties      (positive review - David K -- ask William Stein to confirm: why there is no abelian varieties category and is that a desirable subcategory)
modules                        (100% doctest - David K: many #todo: not implemented -- delete?)
monoid_algebras                (100% doctest - Javier)
number_fields                  (100% doctest - David K: What is the meaning of this coercion?:

Note: A unit group is not a number field (nor a field).  It should coerce into 
a category of groups.

  sage: C = NumberFields()
  sage: C(UnitGroup(NumberField(x^2+1,'a')))  # indirect doctest
  Number Field in a with defining polynomial x^2 + 1)

By this logic one might associate to the integers ZZ the number field QQ,
but I don't see why C(X) should try to find some functor which is not a 
canonical identity on objects.

objects                        (positive reivew - David K)
ordered_monoids                (100% doctest - Javier)
ordered_sets                   (100% doctest - Javier)
pointed_sets                   (100% doctest - David K: the __call__ function is commented out -- should this 
be a not-implemented error?)
principal_ideal_domains        (positive review - Javier)
quotient_fields                (100% doctest - Javier)
right_modules                  (100% doctest - Javier)
ring_ideals                    (100% doctest - Javier)
rings                          (100% doctest - David K: Can the TODO be implemented Rings() == Algebras(ZZ)?)
rngs                           (100% doctest - Javier)
schemes                        (positive review - David K: note that someone might want to revisit this in the future and come up with reasonable subcategories (abelian varieties, etc))
sets_with_partial_maps         (100% doctest - David K: the call function is commented out -- same comment as above; does this call function fall through to the call function on Sets()?)
unique_factorization_domains   (positive review - Javier)
vector_space                   (100% doctest - Javier)