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arXiv · 1810.11188

On truncated quasi-categories

Alexander Campbell·Edoardo Lanari
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Abstract

For each $n \geq -1$, a quasi-category is said to be $n$-truncated if its hom-spaces are $(n-1)$-types. In this paper we study the model structure for $n$-truncated quasi-categories, which we prove can be constructed as the Bousfield localisation of Joyal's model structure for quasi-categories with respect to the boundary inclusion of the $(n+2)$-simplex. Furthermore, we prove the expected Quillen equivalences between categories and $1$-truncated quasi-categories and between $n$-truncated quasi-categories and Rezk's $(n,1)$-$\Theta$-spaces.

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Alexander Campbell, Edoardo Lanari. 2018-10-26. On truncated quasi-categories. https://arxiv.org/abs/1810.11188

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