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groupoid categories
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(Topic)
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Definition 0.1
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 $2$ -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.
The 2-category of groupoids
 , plays a central role in the generalised, categorical Galois theory involving fundamental groupoid functors.
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"groupoid categories" is owned by bci1.
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See Also: 2-category, fundamental groupoid, homeomorphism, higher dimensional algebra, groupoid and group representations related to quantum symmetries, higher dimensional generalized Van Kampen theorems (HD-VKT), groupoids, groupoid homomorphism, quantum fundamental groupoid, category theory, functor category
| Other names: |
category of groupoids, 2-category of groupoids, category of groupoids and groupoid homomorphisms/homeomorphisms |
| Also defines: |
groupoid category, groupoid 2-category |
| Keywords: |
categories of groupoids, homeomorphism, 2-categories, double groupoids, fundamental groupoid functors, extended, categorical Galois theory |
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Cross-references: fundamental groupoid functors, Galois theory, categorical, groupoid homomorphisms, consistent, functors, class, objects, morphisms, invertible, category
There are 15 references to this entry.
This is version 34 of groupoid categories, born on 2008-07-12, modified 2009-02-01.
Object id is 10778, canonical name is GroupoidCategory.
Accessed 2409 times total.
Classification:
| AMS MSC: | 18B40 (Category theory; homological algebra :: Special categories :: Groupoids, semigroupoids, semigroups, groups ) | | | 18G55 (Category theory; homological algebra :: Homological algebra :: Homotopical algebra) | | | 55U40 (Algebraic topology :: Applied homological algebra and category theory :: Topological categories, foundations of homotopy theory) | | | 55U35 (Algebraic topology :: Applied homological algebra and category theory :: Abstract and axiomatic homotopy theory) | | | 55U05 (Algebraic topology :: Applied homological algebra and category theory :: Abstract complexes) |
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Pending Errata and Addenda
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