### Abstract

Language | English |
---|---|

Pages | 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 | |

Publication status | Published - Jan 2020 |

### Fingerprint

### Keywords

- inner anodyne
- quasi-category
- inner fibration
- Weak factorisation system

### Cite this

*Proceedings of the American Mathematical Society*,

*148*(1), 37-40. https://doi.org/10.1090/proc/14692

}

*Proceedings of the American Mathematical Society*, vol. 148, no. 1, pp. 37-40. https://doi.org/10.1090/proc/14692

**A counterexample in quasi-category theory.** / Campbell, Alexander.

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

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

VL - 148

SP - 37

EP - 40

JO - Proceedings of the American Mathematical Society

T2 - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -