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.
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.
Group representations are functors from groups, seen as one-object categories, into FinVect.
DisCoCat models are monoidal functors from a pregroup grammar to FinVect.
See also FinSet ZX-calculus category of modules
References