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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.
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What's a groupoid? What's a good example of a groupoid?
Google Ronald Brown's Topology and Groupoids book for a good introduction and motivation. …
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Geometric interpretation of the fundamental groupoid
Motivation
The common functors from topological spaces to other categories have geometric interpretations. For example, the fundamental group is how loops behave in the space, and higher homotopy grou …