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What is a Higher Level Set?

Tsementzis, Dimitris (2016) What is a Higher Level Set? [Preprint]

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Abstract

Structuralist foundations of mathematics aim for an “invariant” conception of mathematics. But what should be their basic objects? Two leading answers emerge: higher groupoids or higher categories. In this paper I argue in favor of the former over the latter. First, I explain why to pick between them we need to ask the question of what is the correct “categorified” version of a set. Second, I argue in favor of groupoids over categories as “categorified” sets by introducing a pre-formal understanding of groupoids as abstract shapes. This conclusion lends further support to the perspective taken by the Univalent Foundations of mathematics.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Tsementzis, Dimitrisdt506@rci.rutgers.edu
Additional Information: Forthcoming in Philosophia Mathematica
Keywords: Univalent Foundations, Categorification, Structuralism
Subjects: Specific Sciences > Mathematics
Depositing User: Dr. Dimitris Tsementzis
Date Deposited: 05 Nov 2016 19:41
Last Modified: 05 Nov 2016 19:41
Item ID: 12602
Subjects: Specific Sciences > Mathematics
Date: November 2016
URI: http://philsci-archive.pitt.edu/id/eprint/12602

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