ScalingStacks

Fixing $n$, the maps $\Psi_{I\times\partial W_{1};\Sigma(n\bullet),\alpha^{\prime}}$ on various summands in the construction of the skein lasagna module induce a map:

$$\underline{\Psi}_{I\times\partial W_{1};\Sigma(n\bullet),\alpha^{\prime}}\colon\bigoplus_{\alpha\in\langle\alpha^{\prime}\rangle}\underline{\mathcal{S}\mkern-3.0mu}\mkern 3.0mu_{0}^{N,\alpha}(W_{1};K,L)\to\bigoplus_{\alpha\in\langle\alpha^{\prime}\rangle}\underline{\mathcal{S}\mkern-3.0mu}\mkern 3.0mu_{0}^{N,\alpha}(W_{1};K,L)$$

such that

(13)

$$\underline{\Psi}_{I\times\partial W_{1};\Sigma_{-},\alpha^{\prime}}(v\otimes X^{n})=\underline{\Psi}_{I\times\partial W_{1};\Sigma(n\bullet),\alpha^{\prime}}(v).$$