Dissertation/Thesis Abstract

The Category-Theoretical Imperative
by Ernst, Michael, Ph.D., University of California, Irvine, 2014, 114; 3642922
Abstract (Summary)

Category theory has been advocated as a replacement for set theory as the foundation for mathematics. It is claimed that as a foundation set theory is both inadequate and inappropriate. Set theory is considered inadequate because it cannot produce all of the mathematical objects of interest. Set theory is considered inappropriate because it provides a poor framework for mathematical research. In this dissertation, I argue that category theory is subject to exactly the same objections by considering the use of category theory for work in graph theory.

Indexing (document details)
Advisor: Maddy, Penelope
Commitee: Heis, Jeremy, McLarty, Colin, Weatherall, James, Wehmeier, Kai
School: University of California, Irvine
Department: Philosophy.
School Location: United States -- California
Source: DAI-A 76/01(E), Dissertation Abstracts International
Subjects: Mathematics, Philosophy
Keywords: Category theory, Mathematical objects of interest, Poor framework, Set theory
Publication Number: 3642922
ISBN: 978-1-321-30101-4
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