A counterexample in quasi-category theory

Alexander Campbell

doi:10.1090/proc/14692

A counterexample in quasi-category theory

Alexander Campbell

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We give an example of a morphism of simplicial sets which is a monomorphism, bijective on 0-simplices, and a weak categorical equivalence, but which is not inner anodyne. This answers an open question of Joyal. Furthermore, we use this morphism to refute a plausible description of the class of fibrations in Joyal's model structure for quasi-categories.

Original language	English
Pages (from-to)	37-40
Number of pages	4
Journal	Proceedings of the American Mathematical Society
Volume	148
Issue number	1
Early online date	9 Jul 2019
DOIs	https://doi.org/10.1090/proc/14692
Publication status	Published - Jan 2020

Keywords

inner anodyne
quasi-category
inner fibration
Weak factorisation system

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10.1090/proc/14692

https://arxiv.org/abs/1904.04965Licence: Unspecified

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abstract = "We give an example of a morphism of simplicial sets which is a monomorphism, bijective on 0-simplices, and a weak categorical equivalence, but which is not inner anodyne. This answers an open question of Joyal. Furthermore, we use this morphism to refute a plausible description of the class of fibrations in Joyal's model structure for quasi-categories.",

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AB - We give an example of a morphism of simplicial sets which is a monomorphism, bijective on 0-simplices, and a weak categorical equivalence, but which is not inner anodyne. This answers an open question of Joyal. Furthermore, we use this morphism to refute a plausible description of the class of fibrations in Joyal's model structure for quasi-categories.

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KW - quasi-category

KW - inner fibration

KW - Weak factorisation system

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UR - http://purl.org/au-research/grants/arc/DP160101519

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A counterexample in quasi-category theory

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Monoidal categories and beyond: new contexts and new applications

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A counterexample in quasi-category theory

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Monoidal categories and beyond: new contexts and new applications

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