quantum categories
Definition 0.1
A
quantum category

is defined as the (non-Abelian)
category of quantum groupoids,
![$ [Q_{{\mathsf{G}}}]_i$](img2.png)
,
and quantum groupoid homomorphisms,
![$ [q_{{\mathsf{G}}}]_{ij}$](img3.png)
, where

and

are indices in an index class,

, all subject to the usual
ETAC axioms
and their interpretations.
Remark 0.2
A
physical mathematics
definition of quantum category has also been reported as a rigid monoidal category, or its equivalents.
-
- 1
-
Butterfield, J. and C. J. Isham: 2001, Space-time and the
philosophical challenges of quantum gravity., in C. Callender and
N. Hugget (eds. ) Physics Meets Philosophy at the Planck
scale., Cambridge University Press,pp.33-89.
- 2
-
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.
- 3
-
Butterfield, J. and C. J. Isham: 1998, 1999, 2000-2002, A topos
perspective on the Kochen-Specker theorem I - IV, Int. J.
Theor. Phys, 37 No 11., 2669-2733 38 No 3.,
827-859, 39 No 6., 1413-1436, 41 No 4.,
613-639.
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