The MacLane problem on set-theoretical foundations for the category theory
type: Item
instance of: scholarly article
title: The MacLane problem on set-theoretical foundations for the category theory
zbMATH Open document ID: 0970.18001
DOI: 10.1007/BF02673878
published in: Journal of Mathematical Sciences (New York)
publication date: 2001-01-17T00:00:00Z
review text: This paper, a translation from the original Russian [in: Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh. Temat. Obz. 63 (1999)], addresses the problem of devising set-theoretic axioms sufficient for treating naive category theory (including such questionable constructions as functor categories, etc.). The authors review and critique many of the approaches to solving MacLane's problem; and propose one of their own, based on a ``multi-rank theory of classes and sets''.
reviewed by: Paul Bankston
Mathematics Subject Classification ID: 18A15
Mathematics Subject Classification ID: 03B99
Mathematics Subject Classification ID: 03E99
zbMATH DE Number: 1551876
zbMATH Keywords: axiomatic set theory
zbMATH Keywords: multi-rank theory of classes and sets
zbMATH Keywords: naive category theory
zbMATH Keywords: functor categories
zbMATH Keywords: MacLane's problem
author: V. K. Zakharov
author: A. V. Mikhalev
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02673878
OpenAlex ID: W1976527028
description: scientific article; zbMATH DE number 1551876