Blue schemes, semiring schemes, and relative schemes after Toën and Vaquié

Restricted to blue schemes that are locally of finite type over a blue field, we construct an inverse to the Yoneda functor, which establishes an equivalence for this subclass of blue schemes. Moreover, we verify the compatibility of the Yoneda functors with the base extension from blue schemes to semiring schemes and with the base extension from semiring schemes to usual schemes.