Up with categories, down with sets; Out with categories, in with sets!

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Kirby, Jonathan ORCID: https://orcid.org/0000-0003-4031-9107 (2024) Up with categories, down with sets; Out with categories, in with sets! Philosophia Mathematica, 32 (2). 216–227. ISSN 0031-8019

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Abstract

Practical approaches to the notions of subsets and extension sets are compared, coming from broadly set-theoretic and category-theoretic traditions of mathematics. I argue that the set-theoretic approach is the most practical for “looking down” or “in” at subsets and the category-theoretic approach is the most practical for “looking up” or “out” at extensions, and suggest some guiding principles for using these approaches without recourse to either category theory or axiomatic set theory.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Logic (former - to 2024) Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Related URLs:	http://www.scopus.com/inward/record.url?...
Depositing User:	LivePure Connector
Date Deposited:	04 Mar 2024 18:37
Last Modified:	18 Nov 2024 00:55
URI:	https://ueaeprints.uea.ac.uk/id/eprint/94539
DOI:	10.1093/philmat/nkae010

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