Definition 0.1. A quantum category 𝒬 is defined as the (non-Abelian) category of quantum
groupoids, [QG]i, and quantum groupoid homomorphisms, [qG]ij, where i and j are indices in
an index class, I, all subject to the usual ETAC axioms and their interpretations.
Remark 0.1.
The category of quantum groupoids, [QG]i, is trivially a subcategory of the groupoid category,
that can also be regarded as a functor category, or 2-category, if G is small, that is, if G0 is
a set rather than a class.
Remark 0.2. A physical mathematics definition of quantum category has also been reported
as a rigid monoidal category, or its equivalents.
References
[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.
