Some proposals for the set-theoretic foundations of category theory

Authors

DOI:

https://doi.org/10.13130/2037-4445/11085

Abstract

The problem of finding proper set-theoretic foundations for category theory has challenged mathematician since the very beginning. In this paper we give an analysis of some of the standard approaches that have been proposed in the past 70 years. By means of the central notions of class and universe we suggest a possible conceptual recasting of these proposals. We focus on the intended semantics for the (problematic) notion of large category in each proposed foundation. Following Feferman (2006) we give a comparison and evaluation of their expressive power.

Author Biography

  • Lorenzo Malatesta, University of Milan

    Graduate Student in Philosophy, University of Milan

     

    BA in Philosophy, University of Milan, 2012

     

    pietroangelo.casati@gmail.com

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Published

2018-12-31

Issue

Vol. 9 No. 2 (2018): Logic

Section

Special Issue - Articles

License

The authors keep the intellectual property for their work, while the journal owns the exclusive rights concerning the first publication of the articles. The journal will also reserve the rights to create an Open Access archive under the Creative Commons License. Articles are published under a Creative Commons By Attribution License.

How to Cite

Some proposals for the set-theoretic foundations of category theory. (2018). Rivista Italiana Di Filosofia Analitica Junior, 9(2), 117-137. https://doi.org/10.13130/2037-4445/11085