Modeling $(\infty,1)$-categories with Segal spaces

Lyne Moser; Joost Nuiten

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arXiv · 2412.10359

Modeling $(\infty,1)$-categories with Segal spaces

Lyne Moser·Joost Nuiten

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Abstract

In this paper, we construct a model structure for $(\infty,1)$-categories on the category of simplicial spaces, whose fibrant objects are the Segal spaces. In particular, we show that it is Quillen equivalent to the models of $(\infty,1)$-categories given by complete Segal spaces and Segal categories. We furthermore prove that this model structure has desirable properties: it is cartesian closed and left proper. As applications, we get a simple description of the inclusion of categories into $(\infty,1)$-categories and of homotopy limits of $(\infty,1)$-categories.

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BibTeX RIS

Lyne Moser, Joost Nuiten. 2024-12-13. Modeling $(\infty,1)$-categories with Segal spaces. https://arxiv.org/abs/2412.10359

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