Remark 5.6.3. The \(n\)-fold monoids defined above are usually called \(\Ee _n\)-monoids in the literature. Indeed, if \(C\) is equipped with its cartesian symmetric monoidal structure, then \(\Mon ^{(n)}(C)\) can be described as the \(\infty \)-category of algebras over the little \(n\)-cubes \(\infty \)-operad \(\Ee _n\); see [Lurie (2017), Theorem 5.1.2.2 and Proposition 2.4.2.5]. We will not use this description here.
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