Groupoid categories, or categories of groupoids, can be defined simply by considering a groupoid as a category with all invertible morphisms, and objects defined by the groupoid class or set of groupoid elements; then, the groupoid category, , is defined as the -category whose objects are categories (groupoids), and whose morphisms are functors of categories consistent with the definition of groupoid homomorphisms, or in the case of topological groupoids, consistent as well with topological groupoid homeomorphisms (http://planetmath.org/Homeomorphism).
Example 0.1 : The -category of Lie groupoids is an example of a groupoid category, or -category of groupoids.
The -category of Lie groupoids has Lie groupoids as objects, and for any two such objects and there is a hom-category
where is a category whose objects are – bibundles of the Lie groupoids and , respectively over and , and whose morphisms are arrows between such bibundles and that commute with the bundles and
|Date of creation||2013-03-22 18:12:00|
|Last modified on||2013-03-22 18:12:00|
|Last modified by||bci1 (20947)|
|Synonym||category of groupoids|
|Synonym||2-category of groupoids|
|Synonym||category of groupoids and groupoid homomorphisms/homeomorphisms|
|Defines||2-category of groupoids|
|Defines||2-category of Lie groupoids|