Examples of groupoid

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The prototypical example of a groupoid that is not a group is the 'path space' groupoid.
The shortest way to define groupoid is to say it means a small category with inverses.
The second is a closed set called the isotropy bundle, and it will be proved to be a continuous groupoid.
Note that the definition of the groupoid of a polymorphism given in [1] is not correct and should be replaced by this one.
This follows from a similar fact for the right action of a groupoid on itself.
We endow it with a topology that makes it an r -discrete groupoid.
The conditions of the theorem are needed to guarantee that this groupoid has the necessary structure.
Definition 2.2 is easily extended from group actions to groupoid actions.
The reader is invited to check that the map is a groupoid morphism.
A local groupoid is weakly enlargeable if and only if the partial product law is generally associative.
On the basis of these two definitions, we introduce the notion of proper groupoid.
Crossed products by groupoid actions and their smooth flows of weights.
We may assume that this neighbourhood is invariant for the action groupoid.
Any group is a groupoid where the set of its units is reduced to a singleton and vice versa.
Since we are only interested in properties up to null sets, we freely replace a measured groupoid by any of its inessential reductions, if necessary.
The action is clearly free (because the action of a groupoid on itself is free).
If the groupoid is furnished with a topology for which the groupoid operations are continuous then is called a topological groupoid.
We begin by stating a groupoid equivalence result that will be useful in both cases.
These automorphisms respect the structure maps of the groupoid.
In a groupoid such a notion can be defined between different start and end points provided the path can be 'retraced' or 'reverted'.

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