ScalingStacks

We assume now that $\sigma$ is invertible. We define $\tau$ an endomorphism of $(B,A)$-bimodules of $E_{2}^{2}\otimes_{B}A\oplus E_{2}E_{1}\otimes_{B}A\oplus E_{1}E_{2}\otimes_{B}A\oplus E_{1}^{2}\otimes_{B}A$ by

(5.3.4)

$$\tau=\left(\begin{matrix}\tau_{2}\otimes 1&0&0&0\\ 0&0&\sigma^{-1}\otimes 1&0\\ 0&0&0&0\\ 0&0&0&\tau_{1}\otimes 1\end{matrix}\right).$$