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]

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

• FinSet
• ZX-calculus
• category of modules