Globular PROs and the weak ω-categorification of algebraic theories
dc.contributor.author | Bressie, Phillip M. | |
dc.date.accessioned | 2019-06-05T13:36:02Z | |
dc.date.available | 2019-06-05T13:36:02Z | |
dc.date.graduationmonth | August | en_US |
dc.date.issued | 2019-08-01 | |
dc.date.published | 2019 | en_US |
dc.description.abstract | Batanin and Leinster's work on globular operads has provided one of many potential definitions of a weak ω-category. Through the language of globular operads they construct a monad whose algebras encode weak ω-categories. The purpose of this work is to show how to construct a similar monad which will allow us to formulate weak ω-categorifications of any equational algebraic theory. We first review the classical theory of operads and PROs. We then present how Leinster's globular operads can be extended to a theory of globular PROs via categorical enrichment over the category of collections. It is then shown how a process called globularization allows us to construct from a classical PRO P a globular PRO whose algebras are those algebras for P which are internal to the category of strict ω-categories and strict ω-functors. Leinster's notion of a contraction structure on a globular operad is then extended to this setting of globular PROs in order to build a monad whose algebras are globular PROs with contraction over the globularization of the classical PRO P. Among these PROs with contraction over P is the globular PRO whose algebras are by construction the fully weakened ω-categorifications of the algebraic theory encoded by P. | en_US |
dc.description.advisor | David Yetter | en_US |
dc.description.degree | Doctor of Philosophy | en_US |
dc.description.department | Department of Mathematics | en_US |
dc.description.level | Doctoral | en_US |
dc.identifier.uri | http://hdl.handle.net/2097/39788 | |
dc.language.iso | en_US | en_US |
dc.subject | Globular PRO | en_US |
dc.subject | Higher category theory | en_US |
dc.subject | Globular operad | en_US |
dc.subject | Duoidal categories | en_US |
dc.subject | Enriched monoidal categories | en_US |
dc.subject | Monads | en_US |
dc.title | Globular PROs and the weak ω-categorification of algebraic theories | en_US |
dc.type | Dissertation | en_US |