The left-module cut construction

Construction 19.3.3. Define \[ \LCut \colon \simp \catop \times [1]\longrightarrow \oLMod ^{\otimes } \] as the composite \[ \simp \catop \times [1] \xrightarrow {\Cut \times [1]} \Assoc ^{\otimes }\times [1] \longrightarrow \oLMod ^{\otimes }, \] where the final functor sends \((I,1)\) to \((I,\emptyset )\) and \((I,0)\) to \((I,\{m\})\). The morphism from \((I,0)\) to \((I,1)\) is represented by the span \[ (I,\{m\})\hookleftarrow (I,\emptyset )\xrightarrow {=}(I,\emptyset ). \]