PlanetPhysics/Quantum Categories

\newcommand{\sqdiagram}[9]{$$ \diagram #1 \rto^{#2} \dto_{#4}&

\eqno{\mbox{#9}}$$ }

A quantum category $$\Q$$ is defined as the (non-Abelian) category of quantum groupoids, $$[Q_{\grp}]_i$$, and quantum groupoid homomorphisms, $$[q_{\grp}]_{ij}$$, 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, $$[Q_{\grp}]_i$$, is trivially a subcategory of the groupoid category, that can also be regarded as a functor category, or $$2$$-category, if $$\grp$$ 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.