Remarks on $phi$-coordinated modules for quantum vertex algebras

This paper is about $phi$-coordinated modules for weak quantum vertex algebras. Among the main results, several canonical connections among $phi$-coordinated modules for different $phi$ are established. For vertex operator algebras, a reinterpretation of Frenkel-Huang-Lepowskys theorem on contragredient module is given in terms of $phi$-coordinated modules.