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Sep 10, 2015 at 19:43 comment added Qiaochu Yuan @Jon: I think so; it should end up being the homotopy quotient of $G$ by the multiplication action of $H$.
Sep 10, 2015 at 18:34 comment added Jonathan Beardsley Does this construction admit the universal property that we might expect of a quotient?
Sep 10, 2015 at 18:10 vote accept Jonathan Beardsley
Sep 10, 2015 at 23:21
Sep 10, 2015 at 18:10 comment added Jonathan Beardsley This is really nice @Qiaochu, thanks!
Sep 10, 2015 at 16:56 history answered Qiaochu Yuan CC BY-SA 3.0