ScalingStacks

We denote by $\sigma$ the composition

(4.4.1)

$$\sigma:E_{2}E_{1}\xrightarrow{\eta_{1}E_{2}E_{1}}E_{1}F_{1}E_{2}E_{1}\xrightarrow{E_{1}\lambda E_{2}}E_{1}E_{2}F_{1}E_{1}\xrightarrow{E_{1}E_{2}\varepsilon_{1}}E_{1}E_{2}$$

and by $\rho$ the composition

(4.4.2)

$$\rho:F_{1}E_{1}\xrightarrow{F_{1}E_{1}\eta_{1}}F_{1}E_{1}^{2}F_{1}\xrightarrow{F_{1}\tau_{1}F_{1}}F_{1}E_{1}^{2}F_{1}\xrightarrow{\varepsilon_{1}E_{1}F_{1}}E_{1}F_{1}.$$

The diagram (4.3.1) is commutative.