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 $C(\mathcal M)$?
2025-01-12 23:37:05.1736725025
Maximal subcategory inside a multicategory
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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".)