groupoid categories

Definition 0.1   Groupoid categories, or categories of groupoids, can be defined simply by considering a groupoid as a category $ \mathsf{\mathcal G}_1$ with all invertible morphisms, and objects defined by the groupoid class or set of groupoid elements; then, the groupoid category, $ \mathsf{\mathcal G}_2$ , is defined as the $ 2$ -category whose objects are $ \mathsf{\mathcal G}_1$ categories (groupoids), and whose morphisms are functors of $ \mathsf{\mathcal 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{\mathcal G}_2$ , plays a central role in the generalised, categorical Galois theory involving fundamental groupoid functors.



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