Two FRT bialgebroids and their relations

We generalize the FRT construction for the quiver-theoretical quantum Yang-Baxter equation and obtain a left bialgebroid $\mathfrak{A}(w)$. There are some relations between the left bialgebroid $\mathfrak{A}(w)$ and a left bialgebroid $A_{\sigma}$ by the FRT construction for the dynamical Yang-Baxter map.