ScalingStacks

Definition 3.5. The homological grading on $\left\llbracket L^{i}_{\pm}\right\rrbracket$ splits into the sum of the internal and external homological gradings, contributed by resolutions of internal and external crossings respectively. The internal and external homological degrees of a web $W$ appearing in $\left\llbracket L^{i}_{\pm}\right\rrbracket$ will be denoted by $\mathrm{gr}_{\mathrm{int}}(W)$ and $\mathrm{gr}_{\mathrm{ext}}(W)$ respectively.