FinVect
From HandWiki
Short description: The category of finite dimensional vector spaces and linear maps.
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
References
- ↑ 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. doi:10.4204/EPTCS.323.6. https://scholar.googleusercontent.com/scholar.bib?q=info:hHiyaU_p6-AJ:scholar.google.com/&output=citation&scisdr=CgXXiV6NEJT6uebecrw:AAGBfm0AAAAAY3DYarzhswQRNF4gQmnLJCBdh2EDTL0a&scisig=AAGBfm0AAAAAY3DYah8teHAVmBWJPhJ8JmlTXXJ5fXfI&scisf=4&ct=citation&cd=-1&hl=en.
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