ScalingStacks

Starting from here, we see that skein lasagna modules are functorial under inclusions, in the following sense. We consider the case when $Y_{0}=\emptyset$, and we fix a lasagna filling $G$ of $Z$ with boundary $\overline{L}\cup L_{1}$. We can think of $Z$ as a cobordism from $Y=\partial W$ to $Y_{1}$. Then, there is an induced cobordism map

(4)

$$\Psi_{Z;G}=\Psi(\cdot\otimes[G]):\mathcal{S}_{0}^{N}(W;L)\to\mathcal{S}_{0}^{N}(W\cup Z;L_{1}).$$