Realizations Covariant Functorial Construction#
See also
Sets().WithRealizations
for an introduction to realizations and with realizations.sage.categories.covariant_functorial_construction
for an introduction to covariant functorial constructions.sage.categories.examples.with_realizations
for an example.
- class sage.categories.realizations.Category_realization_of_parent(parent_with_realization)[source]#
Bases:
Category_over_base
,BindableClass
An abstract base class for categories of all realizations of a given parent
INPUT:
parent_with_realization
– a parent
See also
EXAMPLES:
sage: A = Sets().WithRealizations().example(); A # needs sage.modules The subset algebra of {1, 2, 3} over Rational Field
>>> from sage.all import * >>> A = Sets().WithRealizations().example(); A # needs sage.modules The subset algebra of {1, 2, 3} over Rational Field
The role of this base class is to implement some technical goodies, like the binding
A.Realizations()
when a subclassRealizations
is implemented as a nested class inA
(see thecode of the example
):sage: C = A.Realizations(); C # needs sage.modules Category of realizations of The subset algebra of {1, 2, 3} over Rational Field
>>> from sage.all import * >>> C = A.Realizations(); C # needs sage.modules Category of realizations of The subset algebra of {1, 2, 3} over Rational Field
as well as the name for that category.
- sage.categories.realizations.Realizations(self)[source]#
Return the category of realizations of the parent
self
or of objects of the categoryself
INPUT:
self
– a parent or a concrete category
Note
this function is actually inserted as a method in the class
Category
(seeRealizations()
). It is defined here for code locality reasons.EXAMPLES:
The category of realizations of some algebra:
sage: Algebras(QQ).Realizations() Join of Category of algebras over Rational Field and Category of realizations of unital magmas
>>> from sage.all import * >>> Algebras(QQ).Realizations() Join of Category of algebras over Rational Field and Category of realizations of unital magmas
The category of realizations of a given algebra:
sage: A = Sets().WithRealizations().example(); A # needs sage.modules The subset algebra of {1, 2, 3} over Rational Field sage: A.Realizations() # needs sage.modules Category of realizations of The subset algebra of {1, 2, 3} over Rational Field sage: C = GradedHopfAlgebrasWithBasis(QQ).Realizations(); C Join of Category of graded Hopf algebras with basis over Rational Field and Category of realizations of Hopf algebras over Rational Field sage: C.super_categories() [Category of graded Hopf algebras with basis over Rational Field, Category of realizations of Hopf algebras over Rational Field] sage: TestSuite(C).run()
>>> from sage.all import * >>> A = Sets().WithRealizations().example(); A # needs sage.modules The subset algebra of {1, 2, 3} over Rational Field >>> A.Realizations() # needs sage.modules Category of realizations of The subset algebra of {1, 2, 3} over Rational Field >>> C = GradedHopfAlgebrasWithBasis(QQ).Realizations(); C Join of Category of graded Hopf algebras with basis over Rational Field and Category of realizations of Hopf algebras over Rational Field >>> C.super_categories() [Category of graded Hopf algebras with basis over Rational Field, Category of realizations of Hopf algebras over Rational Field] >>> TestSuite(C).run()
See also
ClasscallMetaclass
Todo
Add an optional argument to allow for:
sage: Realizations(A, category=Blahs()) # todo: not implemented
>>> from sage.all import * >>> Realizations(A, category=Blahs()) # todo: not implemented
- class sage.categories.realizations.RealizationsCategory(category, *args)[source]#
Bases:
RegressiveCovariantConstructionCategory
An abstract base class for all categories of realizations category
Relization are implemented as
RegressiveCovariantConstructionCategory
. See there for the documentation of how the various bindings such asSets().Realizations()
andP.Realizations()
, whereP
is a parent, work.See also