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] FinVect has two monoidal products: 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]