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Foundations of Unlimited Category Theory

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Title Foundations of Unlimited Category Theory
Title of Series Paul Bernays Lectures 2012
Number of Parts 4
Author Feferman, Solomon
License CC Attribution - NonCommercial - NoDerivatives 2.5 Switzerland:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
DOI 10.5446/36703
Publisher Eidgenössische Technische Hochschule (ETH) Zürich
Release Date 2012
Language English

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Subject Area Mathematics
Abstract Following a discussion of various forms of set-theoretical foundations of category theory and the controversial question of whether category theory does or can provide an autonomous foundation of mathematics, this lecture concentrates on the question whether there is a foundation for “unlimited” or “naïve” category theory. I proposed four criteria for such some years ago. This lecture describes how much had previously been accomplished on one approach to meeting those criteria, then takes care of one important obstacle that had been met in that approach, and finally explains what remains to be done if one is to have a fully satisfactory solution.

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