ScalingStacks

Remark 4.3. Let $\bar{{\mathcal{C}}}=\operatorname{colim}\nolimits{\mathcal{C}}$ and assume there are endofunctors $T_{\pm}$ of $\bar{{\mathcal{C}}}$ which restrict to $T_{S,s,\pm}$ for any $S$ and $s\in S$. Replacing ${\mathcal{C}}_{(W,S)}$ by $\bar{{\mathcal{C}}}$, one can construct from a Markov $2$-trace another one taking value in the constant category $\bar{{\mathcal{C}}}$, and with fixed endofunctors $T_{\pm}$.