Finite Crystals

class sage.categories.finite_crystals.FiniteCrystals(base_category)[source]

Bases: CategoryWithAxiom_singleton

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
>>> from sage.all import *
>>> C = FiniteCrystals()
>>> C
Category of finite crystals
>>> C.super_categories()
[Category of crystals, Category of finite enumerated sets]
>>> C.example()
Highest weight crystal of type A_3 of highest weight omega_1
class TensorProducts(category, *args)[source]

Bases: TensorProductsCategory

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

extra_super_categories()[source]

EXAMPLES:

sage: FiniteCrystals().TensorProducts().extra_super_categories()
[Category of finite crystals]
>>> from sage.all import *
>>> FiniteCrystals().TensorProducts().extra_super_categories()
[Category of finite crystals]
example(n=3)[source]

Return 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
>>> from sage.all import *
>>> B = FiniteCrystals().example(); B
Highest weight crystal of type A_3 of highest weight omega_1
extra_super_categories()[source]

EXAMPLES:

sage: FiniteCrystals().extra_super_categories()
[Category of finite enumerated sets]
>>> from sage.all import *
>>> FiniteCrystals().extra_super_categories()
[Category of finite enumerated sets]