Dear Categorists, In my recent two papers: http://arxiv.org/abs/1207.4246 http://arxiv.org/abs/1211.3204 We came across with something we call "orbifiber bundle". An orbifiber bundle is an orbifold analog of fiber bundle whose fiber and base can be orbifolds. Precise definition is given in Definition2.41 of arXiv:1207.4246. A special case is that the base is a manifold while a fiber is an orbi-vector space, namely vector space with an (effective) finite group action. For example, let the base be S^2, and fiber be the complex plain acted by Z/2Z. An explicit construction of this example using groupoid can be found in this PPT: http://www.math.wisc.edu/~dwang/Dongnings_Homepage_files/SeidelPPT.pdf Generalization of the above example is considered in arXiv:1211.3204. I talked with people who work on orbifolds, and was told this is new. I wonder if this has been studied by any categorist or stack specialist already since it seems so nature. One possible way it occurs is as the following: If G is a group, there is the well-known relation between G-principal bundles and functors from representations of G to G-vector bundles. Now if we replace G with a 2-group and try to make analog of the relation, then the above orbifiber bundles occur. Is there any work done along this direction? And it will be great to know anything else related as well. Thanks in advance! Best Regards Dongning Wang -- PhD candidate Math Dept of UW-Madison www.math.wisc.edu/~dwang [For admin and other information see: http://www.mta.ca/~cat-dist/ ]