The category of necklaces is Reedy monoidal

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 (R op , A) Reedy is monoidal model when equipped with the Day convolution.In the second part, we study the category N ec of necklaces, as defined by Baues and Dugger-Spivak.Making use of a combinatorial description present in Grady-Pavlov and Lowen-Mertens, we streamline some proofs from the literature, and finally show that N ec is simple Reedy monoidal.