# Higher Groupoid Actions, Bibundles, and Differentiation

 dc.contributor.advisor Zhu, Chenchang Prof. Dr. dc.contributor.author Li, Du dc.date.accessioned 2014-08-13T09:23:59Z dc.date.available 2014-08-13T09:23:59Z dc.date.issued 2014-08-13 dc.identifier.uri http://hdl.handle.net/11858/00-1735-0000-0022-5F4F-A dc.identifier.uri http://dx.doi.org/10.53846/goediss-4622 dc.language.iso eng de dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/ dc.subject.ddc 510 de dc.title Higher Groupoid Actions, Bibundles, and Differentiation de dc.type doctoralThesis de dc.contributor.referee Zhu, Chenchang Prof. Dr. dc.date.examination 2014-07-15 dc.description.abstracteng In this thesis, we employ simplicial methods to study actions, principal de bundles and bibundles of higher groupoids. Roughly, we use Kan fibrations to model actions of higher groupoids; we use pairs of a Kan fibration and a special acyclic fibration to model principal bundles of higher groupoids; we use inner Kan fibrations over the interval to model bibundles of higher groupoids. In particular, we show that our definitions given by the simplicial method agree with those given by the categorification approach to actions, principal bundles, and bibundles of 2-groupoids.     In addition, we use the simplicial technique to prove a theorem on differentiation of higher Lie groupoids, which shows that the differentiation functor sends a higher Lie groupoid to a higher Lie algebroid. dc.contributor.coReferee Meyer, Ralf Prof. Dr. dc.subject.eng higher groupoids; higher Lie groupoids; higher groupoid actions; higher groupoid bibundles; differentiation of higher Lie groupoids de dc.identifier.urn urn:nbn:de:gbv:7-11858/00-1735-0000-0022-5F4F-A-2 dc.affiliation.institute Fakultät für Mathematik und Informatik de dc.subject.gokfull Mathematics (PPN61756535X) de dc.identifier.ppn 796514453
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