Bimodules¶
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class
sage.categories.bimodules.
Bimodules
(left_base, right_base, name=None)¶ 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]
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class
ElementMethods
¶
-
class
Bimodules.
ParentMethods
¶
-
Bimodules.
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
Bimodules.
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
-
Bimodules.
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
-
Bimodules.
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
-
Bimodules.
super_categories
()¶ EXAMPLES:
sage: Bimodules(QQ, ZZ).super_categories() [Category of left modules over Rational Field, Category of right modules over Integer Ring]
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class