Tensor Product Functorial Construction¶
AUTHORS:
- Nicolas M. Thiéry (2008-2010): initial revision and refactorization 
- class sage.categories.tensor.TensorProductFunctor[source]¶
- Bases: - CovariantFunctorialConstruction- A singleton class for the tensor functor. - This functor takes a collection of vector spaces (or modules with basis), and constructs the tensor product of those vector spaces. If this vector space is in a subcategory, say that of - Algebras(QQ), it is automatically endowed with its natural algebra structure, thanks to the category- Algebras(QQ).TensorProducts()of tensor products of algebras. For elements, it constructs the natural tensor product element in the corresponding tensor product of their parents.- The tensor functor is covariant: if - Ais a subcategory of- B, then- A.TensorProducts()is a subcategory of- B.TensorProducts()(see also- CovariantFunctorialConstruction). Hence, the role of- Algebras(QQ).TensorProducts()is solely to provide mathematical information and algorithms which are relevant to tensor product of algebras.- Those are implemented in the nested class - TensorProductsof- Algebras(QQ). This nested class is itself a subclass of- TensorProductsCategory.- symbol = ' # '¶
 - unicode_symbol = ' ⊗ '¶
 
- class sage.categories.tensor.TensorProductsCategory(category, *args)[source]¶
- Bases: - CovariantConstructionCategory- An abstract base class for all TensorProducts’s categories. - TensorProducts()[source]¶
- Return the category of tensor products of objects of - self.- By associativity of tensor products, this is - self(a tensor product of tensor products of \(Cat\)’s is a tensor product of \(Cat\)’s)- EXAMPLES: - sage: ModulesWithBasis(QQ).TensorProducts().TensorProducts() Category of tensor products of vector spaces with basis over Rational Field - >>> from sage.all import * >>> ModulesWithBasis(QQ).TensorProducts().TensorProducts() Category of tensor products of vector spaces with basis over Rational Field 
 
- sage.categories.tensor.tensor = The tensor functorial construction[source]¶
- The tensor product functorial construction - See - TensorProductFunctorfor more information- EXAMPLES: - sage: tensor The tensor functorial construction - >>> from sage.all import * >>> tensor The tensor functorial construction