Bases: sage.categories.category.CategoryWithParameters
The category of -bimodules
For and
rings, a
-bimodule
is a left
-module
and right
-module such that the left and right actions commute:
.
EXAMPLES:
sage: Bimodules(QQ, ZZ)
Category of bimodules over Rational Field on the left and Integer Ring on the right
sage: Bimodules(QQ, ZZ).super_categories()
[Category of left modules over Rational Field, Category of right modules over Integer Ring]
Return None.
Indeed, the category of bimodules defines no additional structure: a left and right module morphism between two bimodules is a bimodule morphism.
See also
Todo
Should this category be a CategoryWithAxiom?
EXAMPLES:
sage: Bimodules(QQ, ZZ).additional_structure()
Return an instance of this class.
EXAMPLES:
sage: Bimodules.an_instance()
Category of bimodules over Rational Field on the left and Real Field with 53 bits of precision on the right
Return the left base ring over which elements of this category are defined.
EXAMPLES:
sage: Bimodules(QQ, ZZ).left_base_ring()
Rational Field
Return the right base ring over which elements of this category are defined.
EXAMPLES:
sage: Bimodules(QQ, ZZ).right_base_ring()
Integer Ring
EXAMPLES:
sage: Bimodules(QQ, ZZ).super_categories()
[Category of left modules over Rational Field, Category of right modules over Integer Ring]