On the quotient of a groupoid by an action of a 2-group

Abstract

If X is a groupoid equipped with an action of a 2-group G then one has a 2-groupoid X/G. We describe the fibers of the functor from X/G to the 1-groupoid ${\pi }_0(X)/{\pi }_0(G)$. We also give an explicit model for X/G in a certain situation.

Appendix added