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A proof of the model-independence of $\infty$-category theory Riehl, Emily
Description
In joint work with Dominic Verity we prove that four models of (â ,1)-categories â quasi-categories, complete Segal spaces, Segal categories, and 1-complicial sets â are equivalent for the purpose of developing â -category theory. To prove this we first introduce the notion of an â -cosmos, a category in which â -categories live as objects, an example of which is given by each of the four models mentioned above. We then explain how the category theory of â -categories can be developed inside any â -cosmos; eg, we define right adjoints and limits and prove that the former preserve the latter. We conclude by arguing that the four above mentioned â -cosmoi all biequivalent, the upshot being that â -categorical structures are preserved, reflected, and created by a number of â change-of-modelâ functors. More precisely, we show that each of these â -cosmoi have a biequivalent â calculus of modules,â modules between â -categories being a vehicle to express â -categorical universal properties.
Item Metadata
Title |
A proof of the model-independence of $\infty$-category theory
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2018-05-11T11:30
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Description |
In joint work with Dominic Verity we prove that four models of (â ,1)-categories â quasi-categories, complete Segal spaces, Segal categories, and 1-complicial sets â are equivalent for the purpose of developing â -category theory. To prove this we first introduce the notion of an â -cosmos, a category in which â -categories live as objects, an example of which is given by each of the four models mentioned above. We then explain how the category theory of â -categories can be developed inside any â -cosmos; eg, we define right adjoints and limits and prove that the former preserve the latter. We conclude by arguing that the four above mentioned â -cosmoi all biequivalent, the upshot being that â -categorical structures are preserved, reflected, and created by a number of â change-of-modelâ functors. More precisely, we show that each of these â -cosmoi have a biequivalent â calculus of modules,â modules between â -categories being a vehicle to express â -categorical universal properties.
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Extent |
59.0
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Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Johns Hopkins University
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Series | |
Date Available |
2019-03-25
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0377438
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International