A counterexample in quasi-category theory

Alexander Campbell

Research output: Contribution to journalArticleResearchpeer-review

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.
LanguageEnglish
Pages37-40
Number of pages4
JournalProceedings of the American Mathematical Society
Volume148
Issue number1
Early online date9 Jul 2019
DOIs
Publication statusPublished - Jan 2020

Fingerprint

Category Theory
Morphism
Model structures
Counterexample
Simplicial Set
Monomorphism
Bijective
Fibration
Categorical
Equivalence
Model
Class

Keywords

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

Cite this

Campbell, Alexander. / A counterexample in quasi-category theory. In: Proceedings of the American Mathematical Society. 2020 ; Vol. 148, No. 1. pp. 37-40.
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A counterexample in quasi-category theory. / Campbell, Alexander.

In: Proceedings of the American Mathematical Society, Vol. 148, No. 1, 01.2020, p. 37-40.

Research output: Contribution to journalArticleResearchpeer-review

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