On Noetherian schemes over (\mathcal{C},\otimes,1)$ and the category of quasi-coherent sheaves

Let $(\mathcal C,\otimes,1)$ be an abelian symmetric monoidal category satisfying certain conditions and let $X$ a scheme over in the sense of Toen Vaquie. In this paper we show that when is quasi-compact semi-separated, any quasi-coherent sheaf on may expressed as directed colimit its finitely generated submodules. Thereafter, introduce notion field objects satisfy several properties similar to those fields usual commutative algebra. Finally points Noetherian, semi-separated such object $K$ can recovered from kinds functors between categories sheaves. The latter partial generalization some recent results Brandenburg Chirvasitu.