  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.
