We introduce the inner theory or, more verbosely, isotropy Lawvere theory functor, which generalizes the isotropy group/monoid by assigning a Lawvere theory of coherently extendable arrows to each object of a category with finite powers. Then, we characterize the inner theory for categories of models of an algebraic (or, more generally, quasi-equational) theory, and note its relationship with a notion of definability for morphisms. Finally, we explore a variety of examples.
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/44063 |
| Date | 16 September 2022 |
| Creators | LeBlanc, Frédéric |
| Contributors | Hofstra, Pieter, Scott, Philip |
| Publisher | Université d'Ottawa / University of Ottawa |
| Source Sets | Université d’Ottawa |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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