The MacLane problem on the set-theoretic foundation for category theory. II.
type: Item
instance of: scholarly article
title: The MacLane problem on the set-theoretic foundation for category theory. II.
zbMATH Open document ID: 1037.18001
DOI: 10.1023/A:1021941217859
published in: Journal of Mathematical Sciences (New York)
publication date: 2003-08-15T00:00:00Z
review text: [For part I, see ibid. 102, 4018--4031 (2000; Zbl 0970.18001).] After giving a historical summary of the various ways that axiomatic set theory has failed to provide a satisfactory foundation for naive category theory (e.g., how does one account for the category of all categories), the authors proceed to the syntax and axiomatics of an extension of NBG (von Neumann-Bernays-Gödel set theory), called the two-sorted multi-rank theory of classes and sets. They then proceed to show how naive category theory may be formulated within this framework and finally ask the question of whether their system is a conservative extension of NBG.
Mathematics Subject Classification ID: 18A15
Mathematics Subject Classification ID: 03B99
zbMATH DE Number: 1964709
zbMATH Keywords: axiomatic set theory
zbMATH Keywords: foundations of naive category theory
author: V. K. Zakharov
author: A. V. Mikhalev
reviewed by: Paul Bankston
MaRDI profile type: Publication
full work available at URL: a:1021941217859
OpenAlex ID: W198568404
description: scientific article; zbMATH DE number 1964709