PlanetPhysics/Groupoid Categories

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