See also
Bases: sage.categories.category_types.Category_over_base, sage.misc.bindable_class.BindableClass
An abstract base class for categories of all realizations of a given parent
INPUT:
See also
EXAMPLES:
sage: A = Sets().WithRealizations().example(); A
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 Realizations is implemented as a nested class in A (see the code of the example):
sage: C = A.Realizations(); C
Category of realizations of The subset algebra of {1, 2, 3} over Rational Field
as well as the name for that category.
TESTS:
sage: TestSuite(C).run()
Return the category of realizations of the parent self or of objects of the category self
INPUT:
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 magmas
The category of realizations of a given algebra:
sage: A = Sets().WithRealizations().example(); A
The subset algebra of {1, 2, 3} over Rational Field
sage: A.Realizations()
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()
Todo
Add an optional argument to allow for:
sage: Realizations(A, category = Blahs()) # todo: not implemented
Bases: sage.categories.covariant_functorial_construction.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 as Sets().Realizations() and P.Realizations(), where P is a parent, work.
See also
TESTS:
sage: Sets().Realizations
<bound method Sets_with_category.Realizations of Category of sets>
sage: Sets().Realizations()
Category of realizations of sets
sage: Sets().Realizations().super_categories()
[Category of sets]
sage: Groups().Realizations().super_categories()
[Category of groups, Category of realizations of magmas]