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groupoid categories (Definition)
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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See Also: groupoid homomorphism

Also defines:  groupoid category, category of groupoids
Keywords:  groupoid category

Cross-references: fundamental groupoid functors, 2-category, topological groupoids, groupoid homomorphisms, functors, objects, morphisms, category, groupoid
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This is version 2 of groupoid categories, born on 2009-01-12, modified 2009-01-12.
Object id is 379, canonical name is GroupoidCategories.
Accessed 1099 times total.

Classification:
Physics Classification: 02. (Mathematical methods in physics)
 03. (Quantum mechanics, field theories, and special relativity )
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