Doctoral Dissertations

Keywords and Phrases

Category Theory; Extension Monad; Logic; Nonstandard Analysis; Universal Algebra

Abstract

In this work, we extend the results of finiteness conditions and extension monads found in Insall from finitely many finitary operations to infinitely many finitary operations, as well as touching on infinitary operations. We also examine varieties of algebras, including the notion of strong varieties introduced in Insall, and common constructions of extension monads in varieties of algebras. We see that for finite collections of algebras of the same signature, the extension monad operation on a variety of algebras commutes with the direct product operation, and all retractions from an enlargement or extension monad are trivial. We also see that for any two varieties of algebras which are categorically equivalent, one is strong if and only if the other is strong.

Advisor(s)

Insall, Matt

Committee Member(s)

Wunsch, Donald C.
Akin, Elvan
Murphy, Jason
Wen, Xuerong Meggie

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics and Statistics

Publisher

Missouri University of Science and Technology

Publication Date

Fall 2025

Pagination

iv, 85 pages

Note about bibliography

Includes_bibliographical_references_(pages 82-83)

Rights

© 2025 Danielle Christienne Bowerman , All Rights Reserved

Document Type

Dissertation - Open Access

File Type

text

Language

English

Thesis Number

T 12557

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