PlanetPhysics/Groupoid Categories

Groupoid categories , or categories of groupoids , can be defined

simply by considering a [[../GroupoidHomomorphism2/|groupoid]] as a [[../Cod/|category]] {Failed to parse (unknown function "\G"): {\displaystyle \mathsf{\G}_1} } with all invertible [[../TrivialGroupoid/|morphisms]], and [[../TrivialGroupoid/|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 $2$-category whose objects are Failed to parse (unknown function "\G"): {\displaystyle \mathsf{\G''' _1} } categories (groupoids), and whose morphisms are [[../TrivialGroupoid/|functors]] of Failed to parse (unknown function "\G"): {\displaystyle \mathsf{\G''' _1} } categories consistent with the definition of [[../GroupoidHomomorphism/|groupoid homomorphisms]], or in the case of [[../GroupoidHomomorphism2/|topological groupoids]], consistent as well with topological groupoid homeomorphisms. The [[../2Category/|2-category]] of groupoids Failed to parse (unknown function "\G"): {\displaystyle \mathsf{\G _2} }, plays a central role in the generalised, categorical Galois theory involving [[../QuantumFundamentalGroupoid3/|fundamental groupoid functors]].