Editing Groupoid (section)

==== Finite set ====
Consider the group action of <math>\mathbb{Z}/2</math> on the finite set <math>X = \{-2, -1, 0, 1, 2\}</math> where 1 acts by taking each number to its negative, so <math>-2 \mapsto 2</math> and {{tmath|1= 1 \mapsto -1 }}. The quotient groupoid <math>[X/G]</math> is the set of equivalence classes from this group action {{tmath|1= \{[0],[1],[2]\} }}, and <math>[0]</math> has a group action of <math>\mathbb{Z}/2</math> on it.{{fact|date=May 2025}}