PlanetPhysics/Quantum Categories

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A quantum category  $\mathbb {Q}$ is 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 $i$ and $j$ are indices in an index class, $\mathbf {I}$, 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 $2$-category, if Failed to parse (unknown function "\grp"): {\displaystyle \grp} is small, that is, if $G^{0}$ 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.