A colimit construction for groupoids

Albandik, Suliman

dc.contributor.advisor	Meyer, Ralf Prof. Dr.
dc.contributor.author	Albandik, Suliman
dc.date.accessioned	2016-08-03T08:05:28Z
dc.date.available	2016-08-03T08:05:28Z
dc.date.issued	2016-08-03
dc.identifier.uri	http://hdl.handle.net/11858/00-1735-0000-0028-87E8-C
dc.identifier.uri	http://dx.doi.org/10.53846/goediss-5785
dc.identifier.uri	http://dx.doi.org/10.53846/goediss-5785
dc.identifier.uri	http://dx.doi.org/10.53846/goediss-5785
dc.language.iso	eng	de
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject.ddc	510	de
dc.title	A colimit construction for groupoids	de
dc.type	doctoralThesis	de
dc.contributor.referee	Meyer, Ralf Prof. Dr.
dc.date.examination	2015-08-10
dc.description.abstracteng	We consider Ore monoid actions in a certain bicategory of étale groupoids Gr_prop. Examples of such actions include self-similar groups, higher rank graphs and actions of Ore monoids on spaces by topological correspondences. We prove that every Ore monoid action in Gr_prop has a colimit. We construct a functor from Gr_prop to the bicategory of C-correspondences Corr. We prove that this functor preserves colimits of Ore monoid actions. We write the colimit of an Ore monoid action concretely, and in doing so provide a groupoid model for the Cuntz--Pimsner algebra of the product system associated with the action. In the second part of this thesis, we study colimit equivalence in the bicategories Corr and Gr. We show that under certain assumptions on a diagram, cofinal subdiagrams have equivalent colimits. This generalises the notions of shift equivalences of graphs and C-correspondences.	de
dc.contributor.coReferee	Buss, Alcides Prof. Dr.
dc.subject.eng	colimits	de
dc.subject.eng	bicategories	de
dc.subject.eng	étale groupoid	de
dc.subject.eng	groupoid C*-algebra	de
dc.subject.eng	self-similar group	de
dc.subject.eng	groupoid correspondence	de
dc.subject.eng	Ore monoid	de
dc.subject.eng	topological graph	de
dc.identifier.urn	urn:nbn:de:gbv:7-11858/00-1735-0000-0028-87E8-C-2
dc.affiliation.institute	Fakultät für Mathematik und Informatik	de
dc.subject.gokfull	Mathematik (PPN61756535X)	de
dc.identifier.ppn	869468529

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Fakultät für Mathematik und Informatik (inkl. GAUSS) [518]

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