Inert part of an operad

Remark 14.1.24. More generally, restricting an arbitrary \(\infty \)-operad \(\Oo \) to the subcategory \(\Fin \catop \subseteq \Span (\Fin )\) discards precisely the operations of arity \(\neq 1\): by Lemma 14.1.23, the pullback \(\Oo ^{\otimes } \times _{\Span (\Fin )} \Fin \catop \) is the total category of \(\Triv _{\Oo _{\lra {1}}}\). The resulting projection \(\Triv _{\Oo _{\lra {1}}} \to \Oo \) induces the identity on underlying \(\infty \)-categories, and is thus the counit of the adjunction of Corollary 14.1.21.