PlanetPhysics/Groupoid Action

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Let Failed to parse (unknown function "\grp"): {\displaystyle \grp}
 be a groupoid and $X$ a topological space. A groupoid action , or Failed to parse (unknown function "\grp"): {\displaystyle \grp}
-action, on $X$ is given by two maps: the anchor map  $\pi :X\longrightarrow G_{0}$ and a map $\mu :X\times _{G_{0}}G_{1}\longrightarrow X,$ 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:

• $\pi (xg)=s(g),$
• $xu(\pi (x))=x,$ and
• $(xg)h=x(gh),$ whenever the operations are defined.

{\mathbf Note:} The groupoid action generalizes the concept of group action in a non-trivial way