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Nov 9, 2021 at 20:33 comment added David Roberts No, unfortunately, I hadn't gotten around to that bit. You can cite my thesis, though...
Nov 9, 2021 at 13:21 comment added CuriousUser Thank you David for your answer, I will look into your thesis then. Did you also publish your result in a journal? That would be great for citation purposes.
Nov 9, 2021 at 10:03 comment added David Roberts In my thesis I defined the fundamental bigroupoid of a topological groupoid, and orbifolds can be seen as special cases of these. From this definition one can extract $\pi_2$ of the groupoid, as well as the fundamental group, in the manner of the third definition you give above. I proved that for certain groupoids this gives the expected answer, but not for arbitrary orbifolds, but I expect that proving the classifying space model to be doable.
Nov 8, 2021 at 22:52 history asked CuriousUser CC BY-SA 4.0