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

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.