Categorifying reduced rings

Given a domain of characteristic zero $R$, we functorially construct a rigid symmetric monoidal stable $\mathrm{\infty }$-category whose $K_0$ is $R$, solving a problem of Khovanov. We also functorially construct for any reduced commutative ring $R$ a rigid braided monoidal stable $\mathrm{\infty }$-category whose $K_0$ is $R$.