Using the Countably way below relation, we show that the category $sigma$-CFrm of $sigma$-coherent frames and $sigma$-coherent homomorphisms is coreflective n the category Frm of frames and frame homomorphisms. Introducting the concept of stably countably approximating frames which are exactly retracts of $sigma$-coherent frames, it is shown that the category SCAFrm of stably countably approximating frames and $sigma$-proper frame homomorphisms is coreflective in Frm. Finally we introduce strongly Lindelof frames and show that they are precisely lax retracts of $sigma$-coherent frames.