Английская Википедия:FinVect
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Шаблон:Short description In the mathematical field of category theory, FinVect (or FdVect) is the category whose objects are all finite-dimensional vector spaces and whose morphisms are all linear maps between them.[1]
Properties
FinVect has two monoidal products:
- the direct sum of vector spaces, which is both a categorical product and a coproduct,
- the tensor product, which makes FinVect a compact closed category.
Examples
Tensor networks are string diagrams interpreted in FinVect.[2]
Group representations are functors from groups, seen as one-object categories, into FinVect.[3]
DisCoCat models are monoidal functors from a pregroup grammar to FinVect.[4]
See also
References
