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.

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.

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.

• FinSet
• ZX-calculus
• category of modules