### 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 |
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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 | |

Publication status | Published - Jan 2020 |

### Keywords

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

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## Cite this

Campbell, A. (2020). A counterexample in quasi-category theory.

*Proceedings of the American Mathematical Society*,*148*(1), 37-40. https://doi.org/10.1090/proc/14692