FinVect

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]