O monoid

Definition 14.4.1. Let \(D\) be an \(\infty \)-category with finite products. An \(\Oo \)-monoid in \(D\) is a finite-product-preserving functor \(\Oo ^{\otimes } \to D\). We write \[ \Mon _{\Oo }(D) \quad := \quad \Fun ^{\times }(\Oo ^{\otimes },D) \quad \subseteq \quad \Fun (\Oo ^{\otimes }, D) \] for the full subcategory of \(\Oo \)-monoids in \(D\).