ScalingStacks

$\bullet\$Let $\gamma\in R_{\xi_{1}^{-}}(U,S)$, $\beta\in L_{\xi_{1}^{+}}(V,U)$ and $\alpha\in R_{\xi_{2}^{-}}(T,V)$. We will show that

(8.3.3)

$$\mathrm{action}\circ(\Xi\otimes f_{1})(\alpha\otimes\beta\otimes\gamma)=\bigl(f_{1}\circ R_{\xi_{1}^{-}}(\mathrm{mult}\circ\Xi)\circ\sigma L_{\xi_{1}^{+}}\circ R_{\xi_{2}^{-}}\rho+f_{2}\circ R_{\xi_{2}^{-}}\varepsilon\bigr)(\alpha\otimes\beta\otimes\gamma).$$