# PlanetPhysics/Quantum Fundamental Groupoid 4

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A quantum fundamental groupoid  ${\displaystyle F_{\mathbb {Q} }}$ is defined as a functor ${\displaystyle F_{\mathbb {Q} }:\mathbb {H} _{B}\to {\mathbb {Q} }_{G}}$, where ${\displaystyle {\mathbb {H} }_{B}}$ is the category of Hilbert space bundles, and ${\displaystyle {\mathbb {Q} }_{G}}$ is the category of quantum groupoids and their homomorphisms.

The natural setting for the definition of a quantum fundamental groupoid ${\displaystyle F_{\mathbb {Q} }}$ is in one of the functor categories-- that of fundamental groupoid functors, $\displaystyle F_{\grp}$ , and their natural transformations defined in the context of quantum categories of quantum spaces ${\displaystyle {\mathbb {Q} }}$ represented by Hilbert space bundles or rigged Hilbert (also called Frech\'et) spaces ${\displaystyle {\mathbb {H} }_{B}}$.
Other related functor categories are those specified with the general definition of the fundamental groupoid functor, $\displaystyle F_{\grp}: '''Top''' \to \grp_2$ , where Top is the category of topological spaces and $\displaystyle \grp_2$ is the groupoid category.