PlanetPhysics/Groupoid Action

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Let $$\grp$$ be a groupoid and $$X$$ a topological space. A groupoid action, or $$\grp$$-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