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Mar 11, 2016 at 13:39 comment added André Henriques Concerning "it is quite unfortunate that there does not seem to be a definition of a stack that does not appeal to the functor-of-points-philosophy", you might want to have a look at arxiv.org/pdf/math/0112006v1.pdf. In this little note of mine, I defined an orbifold as a continuous map $E\to X$ whose fibers are $K(\pi,1)$'s. Here, $E$ is the homotopy type of the orbifold, and $X$ is the coarse moduli space of the orbifold.
Jul 12, 2013 at 7:54 comment added Johannes Ebert No, I don't think so.
Jul 11, 2013 at 23:39 comment added Chris Gerig My understanding of (higher) category theory and stacks is absent. But viewing the Pontrjagin-Thom construction in terms of $[M,S^n]$ and cobordism classes of framed submanifolds, is there no analog at this level either?
Jul 10, 2013 at 18:47 history answered Johannes Ebert CC BY-SA 3.0