// Workers AI · dad joke modeWhat did FinVect say to its date? "You vector my heart.
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
[edit]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
[edit]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
[edit]References
[edit]- ↑ Hasegawa, Masahito; Hofmann, Martin; Plotkin, Gordon (2008), "Finite dimensional vector spaces are complete for traced symmetric monoidal categories", Pillars of computer science, Springer, pp. 367–385
- ↑ Kissinger, Aleks (2012). Pictures of processes: automated graph rewriting for monoidal categories and applications to quantum computing (Thesis). arXiv:1203.0202. Bibcode:2012PhDT........17K.
- ↑ Wiltshire-Gordon, John D. (2014-06-03). "Uniformly Presented Vector Spaces". arXiv:1406.0786 [math.RT].
- ↑ de Felice, Giovanni; Meichanetzidis, Konstantinos; Toumi, Alexis (2020). "Functorial question answering". Electronic Proceedings in Theoretical Computer Science. 323: 84–94. arXiv:1905.07408. doi:10.4204/EPTCS.323.6. S2CID 195874109.