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

2 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

Access to Document

10.1090/proc/14692

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

Cite this

@article{1b6948c03ff44c728e48c3d9f5d95a99,

title = "A counterexample in quasi-category theory",

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.",

keywords = "inner anodyne, quasi-category, inner fibration, Weak factorisation system",

author = "Alexander Campbell",

year = "2020",

month = jan,

doi = "10.1090/proc/14692",

language = "English",

volume = "148",

pages = "37--40",

journal = "Proceedings of the American Mathematical Society",

issn = "1088-6826",

publisher = "American Mathematical Society",

number = "1",

}

TY - JOUR

T1 - A counterexample in quasi-category theory

AU - Campbell, Alexander

PY - 2020/1

Y1 - 2020/1

N2 - 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.

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.

KW - inner anodyne

KW - quasi-category

KW - inner fibration

KW - Weak factorisation system

UR - http://www.scopus.com/inward/record.url?scp=85076820565&partnerID=8YFLogxK

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

U2 - 10.1090/proc/14692

DO - 10.1090/proc/14692

M3 - Article

SN - 1088-6826

VL - 148

SP - 37

EP - 40

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 1

ER -

A counterexample in quasi-category theory

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Monoidal categories and beyond: new contexts and new applications

Cite this

A counterexample in quasi-category theory

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Monoidal categories and beyond: new contexts and new applications

Cite this