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On the Unicity of the Homotopy Theory of...

Barwick, Clark...

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On the Unicity of the Homotopy Theory of Higher Categories by Barwick, Clark ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	11-08-2023
Summary	We axiomatise the theory of $(\infty,n)$-categories. We prove that the space of theories of $(\infty,n)$-categories is a $B(\mathbb{Z}/2)^n$. We prove that Rezk's complete Segal $\Theta_n$-spaces, Simpson and Tamsamani's Segal $n$-categories, the first author's $n$-fold complete Segal spaces, Kan and the first author's $n$-relative categories, and complete Segal space objects in any model of $(\infty,n-1)$-categories all satisfy our axioms. Consequently, these theories are all equivalent in a manner that is unique up to the action of $(\mathbb{Z}/2)^n$.
ISBN	-
Item Type	Article
File Type	pdf
File Size	30.00 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1112.0040

Citation

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AMA 11th EditionReferences

Barwick, Clark. On the Unicity of the Homotopy Theory of Higher Categories. Australian National University. August 11, 2023. Accessed October 01, 2025. https://online.provdatabase.com/cite/15769

APA 7th EditionReferences

Barwick, Clark. (2023). On the Unicity of the Homotopy Theory of Higher Categories. Australian National University. https://online.provdatabase.com/cite/15769

Chicago 17th EditionReferences

Barwick, Clark. On the Unicity of the Homotopy Theory of Higher Categories. Australian National University. 2023. https://online.provdatabase.com/cite/15769

HarvardReferences

Barwick, Clark. (2023). On the Unicity of the Homotopy Theory of Higher Categories. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/15769. (Accessed 01 October 2025).

Harvard AustraliaReferences

Barwick, Clark, 2023, On the Unicity of the Homotopy Theory of Higher Categories, Australian National University, viewed 01 October 2025, <https://online.provdatabase.com/cite/15769>

MLA 9th EditionWorks Cited

Barwick, Clark. On the Unicity of the Homotopy Theory of Higher Categories. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/15769.

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