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

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