Realizations Covariant Functorial Construction¶
See also
- Sets().WithRealizationsfor an introduction to realizations and with realizations.
- sage.categories.covariant_functorial_constructionfor an introduction to covariant functorial constructions.
- sage.categories.examples.with_realizationsfor 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 subclass- Realizationsis implemented as a nested class in- A(see the- code 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 - selfor of objects of the category- self- INPUT: - self– a parent or a concrete category
 - Note - this function is actually inserted as a method in the class - Category(see- Realizations()). 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. - Realization are implemented as - RegressiveCovariantConstructionCategory. See there for the documentation of how the various bindings such as- Sets().Realizations()and- P.Realizations(), where- Pis a parent, work.- See also