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Lawvere Theories and Definable Operations

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.

Identiferoai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/44063
Date16 September 2022
CreatorsLeBlanc, Frédéric
ContributorsHofstra, Pieter, Scott, Philip
PublisherUniversité d'Ottawa / University of Ottawa
Source SetsUniversité d’Ottawa
LanguageEnglish
Detected LanguageEnglish
TypeThesis
Formatapplication/pdf

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