Tensor Product Functorial Construction

AUTHORS:

  • Nicolas M. Thiery (2008-2010): initial revision and refactorization
sage.categories.tensor.TensorProductFunctor

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.

The tensor functor is covariant: if A is 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 TensorProducts of Algebras(QQ). This nested class is itself a subclass of TensorProductsCategory.

sage.categories.tensor.TensorProductsCategory

An abstract base class for all TensorProducts’s categories

sage.categories.tensor.tensor = The tensor functorial construction

The tensor product functorial construction

See TensorProductFunctor for more information

EXAMPLES:

sage: tensor
The tensor functorial construction