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

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