PhilSci Archive

What is a Higher Level Set?

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


Download (410kB) | Preview


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.

Export/Citation: EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL
Social Networking:
Share |

Item Type: Preprint
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

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item