# PlanetPhysics/Groupoid Categories

```Groupoid categories , or categories of groupoids , can be defined
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simply by considering a groupoid as a category {$\displaystyle \mathsf{\G}_1$ } with all invertible morphisms, and objects defined by the groupoid class or set of groupoid elements; then, the groupoid category, $\displaystyle \mathsf{\G _2$ }, is defined as the ${\displaystyle 2}$-category whose objects are $\displaystyle \mathsf{\G''' _1$ } categories (groupoids), and whose morphisms are functors of $\displaystyle \mathsf{\G''' _1$ } categories consistent with the definition of groupoid homomorphisms, or in the case of topological groupoids, consistent as well with topological groupoid homeomorphisms. The 2-category of groupoids $\displaystyle \mathsf{\G _2$ }, plays a central role in the generalised, categorical Galois theory involving fundamental groupoid functors.