Definition 0.1. Groupoid categories, or categories of groupoids, can be defined simply
by considering a groupoid as a category 𝒢1 with all invertible morphisms, and objects defined
by the groupoid class or set of groupoid elements; then, the groupoid category, 𝒢2, is defined
as the 2-category whose objects are 𝒢1 categories (groupoids), and whose morphisms are
functors of 𝒢1 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 𝒢2, plays a central role in the generalised, categorical Galois
theory involving fundamental groupoid functors.