From non-colored to colored

Example 12.2.3 (From non-colored to colored). Every non-colored operad \(\Oo \) may be regarded as a colored operad with a single object: we take \(\Oo ^{\simeq } := \{*\}\) and we set \[ \Oo (\underbrace {(*, \dots , *)}_{n \text { times}}; *) := \Oo (n). \] From now on, we will abuse notation and regard non-colored operads as colored operads in this way. In particular, we obtain colored operads \(\Assoc \), \(\Comm \), \(\Lie \) and \(\Ee _k\).