ScalingStacks

Definition 3.7. If $i\in\{0,1,\cdots,x\}$, $\epsilon\in\{+,-\}$, $s\in\{p,t\}^{2n}$, $o\in\{p,t\}$ and $\tau\in\{p,t\}^{M}$, we will use $W_{\epsilon}^{i}(\tau,o,s)$ or $W_{\epsilon}^{i}(\tau,o)$ to denote the web in $\left\llbracket L_{\epsilon}^{i}\right\rrbracket$ with indexing data $(\tau,o,s)$ or $(\tau,o)$, as appropriate. Analogously, we write $W(\tau)$ and $W^{\prime}(\tau)$ for $\tau$-indexed webs in $\left\llbracket L\right\rrbracket$ and $\left\llbracket L^{\prime}\right\rrbracket$ respectively. If the indexing data is fixed, we will sometimes omit it from the notation (e.g. $W^{i}_{\pm}=W^{i}_{\pm}(\tau,o,s)$ and $W=W(\tau)$) and say that the webs $W^{i}_{+}$ and $W^{i}_{-}$ correspond to each other.

If $f$ is a chain map and $V$ and $W$ are webs in the source and target complexes, then we write $f(V,W)$ for the component of $f$ from $V$ to $W$.