Models for rational $(\infty, 1)$-categories

We introduce rational $(\infty, 1)$-categories, which are $(\infty, 1)$-categories enriched in spaces whose higher homotopy groups are rational vector spaces. We provide two models for rational $(\infty, 1)$-categories, rational complete Segal spaces and rational Segal categories, and we show that they are equivalent.

Publication Details

Journal
ArXiv.org
Published
2025-09-26
Primary Topic
Statistical Methods and Inference
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article

Models for rational $(\infty, 1)$-categories

ArXiv.org
Statistical Methods and Inference
article

Models for rational $(\infty, 1)$-categories

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Abstract

We introduce rational $(\infty, 1)$-categories, which are $(\infty, 1)$-categories enriched in spaces whose higher homotopy groups are rational vector spaces. We provide two models for rational $(\infty, 1)$-categories, rational complete Segal spaces and rational Segal categories, and we show that they are equivalent.

ArXiv.org
Openalex Percentile: Top 40%
Statistical Methods and Inference
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Models for rational $(\infty, 1)$-categories · ArXiv.org (2025) | TGRS Research Map | TGRS