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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 𝒢1 with all invertible morphisms, and objects defined by the groupoid class or set of groupoid elements; then, the groupoid category, 𝒢2, is defined as the 2-category whose objects are 𝒢1 categories (groupoids), and whose morphisms are functors of 𝒢1 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 𝒢2, 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, category, groupoid
There are 16 references to this object.

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 3519 times total.

Classification:
Physics Classification02. (Mathematical methods in physics)
 03. (Quantum mechanics, field theories, and special relativity )
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