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.
Read more about this topic: Group Action
Famous quotes containing the words group and/or actions:
“We often overestimate the influence of a peer group on our teenager. While the peer group is most influential in matters of taste and preference, we parents are most influential in more abiding matters of standards, beliefs, and values.”
—David Elkind (20th century)
“The legislative powers of government reach actions only, and not opinions, ... thus building a wall of separation between Church and State.”
—Thomas Jefferson (1743–1826)