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Results tagged with groupoids
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user 184
A groupoid is a category where all morphisms are invertible. This notion can also be seen as an extension of the notion of group. A motivating example is the fundamental groupoid of a topological space with respect to several base points, compared to the usual fundamental group.
6
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Representation of Groupoids
In fact the inclusion of the sub-2-category of disjoint unions of groups into all groupoids is an equivalence. Hence the representation theory of groupoids reduces to that of groups. …
- 27.5k
19
votes
3
answers
605
views
Characterizing Groupoids via Quotients?
.(*) The groupoids form a very nice subclass of categories. The inclusion of the groupoids into the 2-category of small categories admits both left and right (weak) adjoints. … If true, I think this would give a very neat characterization of the groupoids. …
- 27.5k
8
votes
Accepted
What is the 2-category whose 0-objects are Lie algebroids?
These are equivalent groupoids in the bibundle bicategory and so must be sent to equivalent Lie algebroids. … (In a certain sense the bibundle bicategory is what you get when you take Lie groupoids, functors, etc. and force these two types of groupoids to be equivalent. More on this below.) …
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