groupoid action
Definition 0.1.
Let $\mathcal{G}$ be a groupoid^{} and $X$ a topological space^{}. A groupoid action, or $\mathcal{G}$action, on $X$ is given by two maps: the anchor map $\pi :X\u27f6{G}_{0}$ and a map $\mu :X{\times}_{{G}_{0}}{G}_{1}\u27f6X,$ with the latter being defined on pairs $(x,g)$ such that $\pi (x)=t(g)$, written as $\mu (x,g)=xg$. The two maps are subject to the following conditions:

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$\pi (xg)=s(g),$

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$xu(\pi (x))=x,$ and

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$(xg)h=x(gh),$ whenever the operations are defined.
Note: The groupoid action generalizes the concept of group action in a nontrivial way.
Title  groupoid action 
Canonical name  GroupoidAction 
Date of creation  20130322 19:19:23 
Last modified on  20130322 19:19:23 
Owner  bci1 (20947) 
Last modified by  bci1 (20947) 
Numerical id  9 
Author  bci1 (20947) 
Entry type  Definition 
Classification  msc 22A22 
Classification  msc 18B40 
Synonym  action 
Related topic  GroupAction 
Related topic  Groupoid 
Related topic  GroupoidRepresentation4 
Defines  anchor map 