Group Actions and Groupoids
The notion of group action can be put in a broader context by using the action groupoid associated to the group action, thus allowing techniques from groupoid theory such as presentations and fibrations. Further the stabilisers of the action are the vertex groups, and the orbits of the action are the components, of the action groupoid. For more details, see the book Topology and groupoids referenced below.
This action groupoid comes with a morphism which is a covering morphism of groupoids. This allows a relation between such morphisms and covering maps in topology.
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Famous quotes containing the words group and/or actions:
“A little group of willful men, representing no opinion but their own, have rendered the great government of the United States helpless and contemptible.”
—Woodrow Wilson (1856–1924)
“If you need a certain vitality you can only supply it yourself, or there comes a point, anyway, when no one’s actions but your own seem dramatically convincing and justifiable in the plot that the number of your days concocts.”
—John Ashbery (b. 1927)