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The Simplicial Model of Univalent Founda...

Kapulkin, Chris...

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The Simplicial Model of Univalent Foundations (after Voevodsky) by Kapulkin, Chris ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	27-07-2023
Summary	We present Voevodsky's construction of a model of univalent type theory in the category of simplicial sets. To this end, we first give a general technique for constructing categorical models of dependent type theory, using universes to obtain coherence. We then construct a (weakly) universal Kan fibration, and use it to exhibit a model in simplicial sets. Lastly, we introduce the Univalence Axiom, in several equivalent formulations, and show that it holds in our model. As a corollary, we conclude that Martin-L\"of type theory with one univalent universe (formulated in terms of contextual categories) is at least as consistent as ZFC with two inaccessible cardinals.
ISBN	-
Item Type	Article
File Type	pdf
File Size	29.34 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1211.2851

Citation

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AMA 11th EditionReferences

Kapulkin, Chris. The Simplicial Model of Univalent Foundations (after Voevodsky). Australian National University. July 27, 2023. Accessed September 20, 2024. https://online.provdatabase.com/cite/5762

APA 7th EditionReferences

Kapulkin, Chris. (2023). The Simplicial Model of Univalent Foundations (after Voevodsky). Australian National University. https://online.provdatabase.com/cite/5762

Chicago 17th EditionReferences

Kapulkin, Chris. The Simplicial Model of Univalent Foundations (after Voevodsky). Australian National University. 2023. https://online.provdatabase.com/cite/5762

HarvardReferences

Kapulkin, Chris. (2023). The Simplicial Model of Univalent Foundations (after Voevodsky). [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/5762. (Accessed 20 September 2024).

Harvard AustraliaReferences

Kapulkin, Chris, 2023, The Simplicial Model of Univalent Foundations (after Voevodsky), Australian National University, viewed 20 September 2024, <https://online.provdatabase.com/cite/5762>

MLA 9th EditionWorks Cited

Kapulkin, Chris. The Simplicial Model of Univalent Foundations (after Voevodsky). Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/5762.

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