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Question. Let $M$ be a triangulated non-orientable 3-manifold with non-orientable boundary. (It is possible to assume that the boundary is the Klein bottle.) Let $\ell$ be a non-orientable loop on the ...

It is well knows that for a nice (locally path connected, semi-locally simply connected) topological spaces, the category of covering spaces over $X$ is equivalent to the functor category $\left[\Pi_1\...