Cartesian Double Categories with an Emphasis on Characterizing Spans
Date
2018-08-23T17:06:25Z
Authors
Aleiferi, Evangelia
Journal Title
Journal ISSN
Volume Title
Publisher
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.
Description
Keywords
Cartesian bicategories, Cartesian double categories, Fibrant double categories, Spans, Profunctors