Cartesian Double Categories with an Emphasis on Characterizing Spans
dc.contributor.author | Aleiferi, Evangelia | |
dc.contributor.copyright-release | Not Applicable | en_US |
dc.contributor.degree | Doctor of Philosophy | en_US |
dc.contributor.department | Department of Mathematics & Statistics - Math Division | en_US |
dc.contributor.ethics-approval | Not Applicable | en_US |
dc.contributor.external-examiner | Dr. Simon Willerton | en_US |
dc.contributor.graduate-coordinator | Dr. David Iron | en_US |
dc.contributor.manuscripts | Not Applicable | en_US |
dc.contributor.thesis-reader | Dr. Robert Paré | en_US |
dc.contributor.thesis-reader | Dr. Julien Ross | en_US |
dc.contributor.thesis-supervisor | Dr. Geoffrey Cruttwell | en_US |
dc.contributor.thesis-supervisor | Dr. Richard Wood | en_US |
dc.date.accessioned | 2018-08-23T17:06:25Z | |
dc.date.available | 2018-08-23T17:06:25Z | |
dc.date.defence | 2018-08-20 | |
dc.date.issued | 2018-08-23T17:06:25Z | |
dc.description.abstract | In this thesis, we introduce Cartesian double categories, motivated by the work of Carboni, Kelly, Walters, and Wood on Cartesian bicategories. Moving from bicategories to the slightly more generalized notion of double categories allows us to set the whole theory inside the welcoming 2-category of double categories, and to overcome technical problems that were caused by working with left adjoints inside a general bicategory. Cartesian double categories that are also fibrant are of particular interest to us. After describing some important properties of Cartesian and fibrant double categories, we give a characterization of the double category of Spans as a Cartesian double category. Lastly, we talk about profunctors and give a potential framework for their characterization as Cartesian double categories. | en_US |
dc.identifier.uri | http://hdl.handle.net/10222/74133 | |
dc.language.iso | en | en_US |
dc.subject | Cartesian bicategories | en_US |
dc.subject | Cartesian double categories | en_US |
dc.subject | Fibrant double categories | en_US |
dc.subject | Spans | en_US |
dc.subject | Profunctors | en_US |
dc.title | Cartesian Double Categories with an Emphasis on Characterizing Spans | en_US |
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