# PlanetPhysics/Quantum Categories

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Aquantum categoryis defined as the (non-Abelian) category of quantum groupoids,Failed to parse (unknown function "\grp"): {\displaystyle [Q_{\grp}]_i},and quantum groupoid homomorphisms,Failed to parse (unknown function "\grp"): {\displaystyle [q_{\grp}]_{ij}}, where and are indices in an index class, , all subject to the usual ETAC axioms and their interpretations.

The category of quantum groupoids, **Failed to parse (unknown function "\grp"): {\displaystyle [Q_{\grp}]_i}**
, is trivially a subcategory of the groupoid category, that can also be regarded as a functor category, or -category, if **Failed to parse (unknown function "\grp"): {\displaystyle \grp}**
is small, that is, if is a set rather than a class.

A physical mathematics definition of quantum category has also been reported as a rigid monoidal category, or its equivalents.

## All SourcesEdit

^{[1]}^{[2]}^{[3]}

## ReferencesEdit

- ↑ Butterfield, J. and C. J. Isham: 2001, Space-time and the philosophical challenges of quantum gravity., in C. Callender and N. Hugget (eds. ) \emph{Physics Meets Philosophy at the Planck scale.}, Cambridge University Press,pp.33--89.
- ↑
Baianu, I.C.: 1971a, Categories, Functors and Quantum Algebraic Computations, in P. Suppes (ed.),
*Proceed. Fourth Intl. Congress Logic-Mathematics-Philosophy of Science*, September 1--4, 1971, the University of Bucharest. - ↑
Butterfield, J. and C. J. Isham: 1998, 1999, 2000--2002, A topos
perspective on the Kochen--Specker theorem I - IV, \emph{Int. J.
Theor. Phys},
**37**No 11., 2669--2733**38**No 3., 827--859,**39**No 6., 1413--1436,**41**No 4., 613--639.