A counterexample in quasi-category theory

Alexander Campbell

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    1 Citation (Scopus)


    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 languageEnglish
    Pages (from-to)37-40
    Number of pages4
    JournalProceedings of the American Mathematical Society
    Issue number1
    Early online date9 Jul 2019
    Publication statusPublished - Jan 2020


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


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