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