Notes on the Joyal model structure

Danny Stevenson

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arXiv · 1810.05233

Notes on the Joyal model structure

Danny Stevenson

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Abstract

We give a new construction of the Joyal model structure on the category of simplicial sets, and we provide a simple characterization of the fibrations in it. We characterize the inner anodyne maps in terms of categorical equivalences and use this characterization to establish the inner model structure on the category of simplicial sets whose set of zero-simplices is equal to a fixed set $O$.

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Danny Stevenson. 2018-10-11. Notes on the Joyal model structure. https://arxiv.org/abs/1810.05233

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