If G is a (discrete 1-)group, then any G-set decomposes uniquely as a coproduct of transitive G-sets, each of which is the quotient of G by a subgroup. Is something analogous true for actions of 2-groups on groupoids, or for n-groups on (n-1)-groupoids? I remember there was a lot of Cafe discussion about higher Klein geometry, subgroups and homogeneous spaces of higher groups, but I donâ€™t remember whether something like this came up.

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