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# Finite Crystals

class `sage.categories.finite_crystals.``FiniteCrystals`(base_category)

  Bases: `sage.categories.category_with_axiom.CategoryWithAxiom`

  The category of finite crystals.

  EXAMPLES:

      sage: C = FiniteCrystals()
      sage: C
      Category of finite crystals
      sage: C.super_categories()
      [Category of crystals, Category of finite enumerated sets]
      sage: C.example()
      Highest weight crystal of type A_3 of highest weight omega_1

  TESTS:

      sage: TestSuite(C).run()
      sage: B = FiniteCrystals().example()
      sage: TestSuite(B).run(verbose = True)
      running ._test_an_element() . . . pass
      running ._test_category() . . . pass
      running ._test_elements() . . .
        Running the test suite of self.an_element()
        running ._test_category() . . . pass
        running ._test_eq() . . . pass
        running ._test_not_implemented_methods() . . . pass
        running ._test_pickling() . . . pass
        running ._test_stembridge_local_axioms() . . . pass
        pass
      running ._test_elements_eq_reflexive() . . . pass
      running ._test_elements_eq_symmetric() . . . pass
      running ._test_elements_eq_transitive() . . . pass
      running ._test_elements_neq() . . . pass
      running ._test_enumerated_set_contains() . . . pass
      running ._test_enumerated_set_iter_cardinality() . . . pass
      running ._test_enumerated_set_iter_list() . . . pass
      running ._test_eq() . . . pass
      running ._test_fast_iter() . . . pass
      running ._test_not_implemented_methods() . . . pass
      running ._test_pickling() . . . pass
      running ._test_some_elements() . . . pass
      running ._test_stembridge_local_axioms() . . . pass

  class `TensorProducts`(category, *args)

    Bases: `sage.categories.tensor.TensorProductsCategory`

    The category of finite crystals constructed by tensor product of finite crystals.

    `extra_super_categories`()

      EXAMPLES:

          sage: FiniteCrystals().TensorProducts().extra_super_categories()
          [Category of finite crystals]

  `FiniteCrystals.``example`(n=3)

    Returns an example of highest weight crystals, as per `Category.example()`.

    EXAMPLES:

        sage: B = FiniteCrystals().example(); B
        Highest weight crystal of type A_3 of highest weight omega_1

  `FiniteCrystals.``extra_super_categories`()

    EXAMPLES:

        sage: FiniteCrystals().extra_super_categories()
        [Category of finite enumerated sets]

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