# PlanetPhysics/Groupoid Categories

Groupoid categories, orcategories of groupoids, can be defined

simply by considering a groupoid as a category {**Failed to parse (unknown function "\G"): {\displaystyle \mathsf{\G}_1}**
} with all invertible morphisms, and objects defined by the groupoid class or set of groupoid elements; then, the groupoid category, ** Failed to parse (unknown function "\G"): {\displaystyle \mathsf{\G _2}
**},
is defined as the

*-category*whose objects are

**Failed to parse (unknown function "\G"): {\displaystyle \mathsf{\G''' _1}**} categories (groupoids), and whose morphisms are functors of**Failed to parse (unknown function "\G"): {\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

**}, plays a central role in the generalised, categorical Galois theory involving fundamental groupoid functors.**

**Failed to parse (unknown function "\G"): {\displaystyle \mathsf{\G _2}**