Action groupoid


In mathematics, an action groupoid or a transformation groupoid is a groupoid that expresses a group action. Namely, given a group action
we get the groupoid where
A groupoid is often depicted using two arrows. Here the above can be written as:
where denote the source and the target of a morphism in ; thus, is the projection and is the given group action.

In an ∞-category

Let be an ∞-category and a groupoid object in it. Then a group action or an action groupoid on an object X in C is the simplicial diagram
that satisfies the axioms similar to an action groupoid in the usual case.

Works cited