0PC6 Lemma 8.1.2. Given S⊂MS\subset M and n≥0n\geq 0, there is an isomorphism of functors 𝒮M∙(Z)→Sets∙{\mathcal{S}}^{\bullet}_{M}(Z)\to\operatorname{Sets}\nolimits^{\bullet} (forgetting the differential) ⋁S′⊂S|S′|=nHom𝒮∙(Z)(S′,{ξ(1),…,ξ(n)})∧Hom𝒮∙(Z)(S∖S′,−)\displaystyle\bigvee_{\begin{subarray}{c}S^{\prime}\subset S\\ |S^{\prime}|=n\end{subarray}}\operatorname{Hom}\nolimits_{{\mathcal{S}}^{\bullet}(Z)}(S^{\prime},\{\xi(1),\ldots,\xi(n)\})\wedge\operatorname{Hom}\nolimits_{{\mathcal{S}}^{\bullet}(Z)}(S\setminus S^{\prime},-) →∼L∙(−,S,en)\displaystyle\mathrel{\mathop{\kern 0.0pt\to}\limits^{\sim}}L^{\bullet}(-,S,e^{n}) (α,β)\displaystyle(\alpha,\beta) ↦α⊠β.\displaystyle\mapsto\alpha\boxtimes\beta.