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arXiv · 2111.06512

Generalizing quasi-categories via model structures on simplicial sets

Matthew Feller
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Abstract

We use Cisinski's machinery to construct and study model structures on the category of simplicial sets whose classes of fibrant objects generalize quasi-categories. We identify a lifting condition which captures the homotopical behavior of quasi-categories without the algebraic aspects and show that there is a model structure whose fibrant objects are precisely those which satisfy this condition. We also identify a localization of this model structure whose fibrant objects satisfy a "special horn lifting" condition similar to the one satisfied by quasi-categories. This special horn model structure leads to a conjecture characterization of the bijective-on-0-simplices trivial cofibrations of the Joyal model structure. We also discuss how these model structures all relate to one another and to the minimal model structure.

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BibTeXRIS

Matthew Feller. 2021-11-12. Generalizing quasi-categories via model structures on simplicial sets. https://doi.org/10.2140/agt.2025.25.357

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