0PCQ Remark 8.1.17. There is a bifunctorial injective map Rξ−∙(T,−)∧Lξ+∙(−,S)→Hom(S⊔{ξ−(−1)},T⊔{ξ+(1)}),β∧α↦(β⊠idξ+(1))⋅(α⊠idξ−(−1)).R_{\xi^{-}}^{\bullet}(T,-)\wedge L_{\xi^{+}}^{\bullet}(-,S)\to\operatorname{Hom}\nolimits(S\sqcup\{\xi^{-}(-1)\},T\sqcup\{\xi^{+}(1)\}),\ \beta\wedge\alpha\mapsto(\beta\boxtimes\operatorname{id}\nolimits_{\xi^{+}(1)})\cdot(\alpha\boxtimes\operatorname{id}\nolimits_{\xi^{-}(-1)}). The composition of the unit given by Lemma 8.1.16 with this map is the following map Hom(S,T)→Hom(S⊔{ξ−(−1)},T⊔{ξ+(1)}),γ↦(γ⊗idξ+(1))⋅d(ξ~([−1→1])⊠idS).\operatorname{Hom}\nolimits(S,T)\to\operatorname{Hom}\nolimits(S\sqcup\{\xi^{-}(-1)\},T\sqcup\{\xi^{+}(1)\}),\ \gamma\mapsto(\gamma\otimes\operatorname{id}\nolimits_{\xi^{+}(1)})\cdot d(\tilde{\xi}([-1\to 1])\boxtimes\operatorname{id}\nolimits_{S}).