Universal Monoidal Categories with Duals

FieldValue
dc.contributor.authorPilon, Samuel
dc.date.accessioned2021-01-13T14:29:44Z
dc.date.available2021-01-13T14:29:44Z
dc.date.issued2021-01-13
dc.identifier.urihttp://hdl.handle.net/10393/41664
dc.identifier.urihttp://dx.doi.org/10.20381/ruor-25886
dc.description.abstractString diagrams form a diagrammatic notation used in many domains. To understand the simplest diagrams that express some properties, we can look at universal categories. These satisfy universal properties and can be described by presentations in terms of generators and relations. In this thesis, we examine some examples of universal categories, namely the (oriented) Temperley-Lieb and (oriented) Brauer categories. These are respectively the free linear monoidal category on a self-dual object or pair of dual objects, and the free linear symmetric monoidal category on a symmetrically self-dual object or pair of dual objects. Then, to make precise the connection between presentations and universal properties, we exhibit an adjoint functor from a category of generators and relations to the category of linear monoidal categories. We also suggest a general recipe to find a presentation of the category satisfying a specific universal property. Our main goal is to better understand the links between string diagrams, representation theory, generators and relations, and universal properties.
dc.language.isoen
dc.publisherUniversité d'Ottawa / University of Ottawa
dc.subjectString diagrams
dc.subjectTemperley-Lieb category
dc.subjectBrauer category
dc.subjectUniversal categories
dc.subjectUniversal properties
dc.subjectRepresentation theory
dc.subjectMonoidal categories
dc.subjectDual objects
dc.subjectAdjoint functors
dc.titleUniversal Monoidal Categories with Duals
dc.typeThesis
dc.contributor.supervisorSavage, Alistair
thesis.degree.nameMSc
thesis.degree.levelMasters
thesis.degree.disciplineSciences / Science
uottawa.departmentMathématiques et statistique / Mathematics and Statistics
CollectionThèses, 2011 - // Theses, 2011 -

Files