PlanetPhysics/Groupoid Action

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Let Failed to parse (unknown function "\grp"): {\displaystyle \grp}
 be a [[../GroupoidHomomorphism2/|groupoid]] and $X$ a [[../CoIntersections/|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  $\pi :X⟶G_0$ and a map $\mu :X{\times }_{G_0}{G}_1⟶X,$ 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 [[../Cod/|operations]] are defined.

{\mathbf Note:} The groupoid action generalizes the [[../PreciseIdea/|concept]] of [[../TrivialGroupoid/|group]] action in a non-trivial way