Maximal subcategory inside a multicategory

Question

Let $\mathcal M$ be a multicategory. Let $C(\mathcal M)$ be a category consisting of all objects and all unary multimorphisms of $\mathcal M$.

Is there a standard name for $C(\mathcal M)$?

Answer 1

It is called the "underlying category of $\mathcal{M}$" in Lurie's Higher Algebra (Remark 2.1.1.2). I don't know how standard this terminology is, it probably depends on who you ask; I've seen it used at least another time (I don't remember where exactly though).

(Personally I would probably just call that "the category of unary operations".)