Bimodules#
- class sage.categories.bimodules.Bimodules(left_base, right_base, name=None)#
Bases:
CategoryWithParameters
The category of \((R,S)\)-bimodules
For \(R\) and \(S\) rings, a \((R,S)\)-bimodule \(X\) is a left \(R\)-module and right \(S\)-module such that the left and right actions commute: \(r*(x*s) = (r*x)*s\).
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]
- class ElementMethods#
Bases:
object
- class ParentMethods#
Bases:
object
- additional_structure()#
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()
- classmethod an_instance()#
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
- left_base_ring()#
Return the left base ring over which elements of this category are defined.
EXAMPLES:
sage: Bimodules(QQ, ZZ).left_base_ring() Rational Field
- right_base_ring()#
Return the right base ring over which elements of this category are defined.
EXAMPLES:
sage: Bimodules(QQ, ZZ).right_base_ring() Integer Ring
- super_categories()#
EXAMPLES:
sage: Bimodules(QQ, ZZ).super_categories() [Category of left modules over Rational Field, Category of right modules over Integer Ring]