  In the first part of this note we further the study of the interactions
between Reedy and monoidal structures on a small category, building upon the
work of Barwick. We define a Reedy monoidal category as a Reedy category
$\mathcal{R}$ which is monoidal such that for all symmetric monoidal model
categories $\textbf{A}$, the category
$\mathrm{Fun}\left(\mathcal{R}^{\mathrm{op}},
\textbf{A}\right)_{\mathrm{Reedy}}$ is model monoidal when equipped with the
Day convolution. In the second part, we study the category $\mathcal{N}ec$ of
necklaces, as defined by Baues and Dugger-Spivak. Making use of the
combinatorial description present in arXiv:2302.02484v1, we streamline some
proofs from the literature, and finally show that $\mathcal{N}ec$ is simple
Reedy monoidal.
