Left and right module suboperads

Observation 19.2.2. We identify \(\oLMod \) with the full suboperad of \(\oBMod \) spanned by the colors \(\fa _-\) and \(\fm \), and let \(\oRMod \subseteq \oBMod \) denote the full suboperad spanned by \(\fm \) and \(\fa _+\). Thus \(\oBMod \) contains two copies of \(\Assoc \), on \(\fa _-\) and \(\fa _+\), a copy of \(\Triv \) on \(\fm \), and the full suboperads \(\oLMod \) and \(\oRMod \). There is also an operad map \[ \oBMod \longrightarrow \Assoc \] which sends all three colors to \(\fa \) and forgets the restrictions on the linear orders. Its restrictions to \(\oLMod \) and \(\oRMod \) are the usual collapse maps to \(\Assoc \).