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
R which is monoidal such that for all symmetric monoidal model
categories A, the category
Fun(Rop,A)Reedy​ is model monoidal when equipped with the
Day convolution. In the second part, we study the category Nec 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 Nec is simple
Reedy monoidal.Comment: 15 pages, no figures, comments welcome; v2: removed typos, changed
notation, updated acknowledgement