The category of necklaces is Reedy monoidal

Violeta Borges Marques and Arne Mertens

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 Nec 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 Nec is simple Reedy monoidal.

Keywords: Reedy category, necklaces, monoidal model category

2020 MSC: 18M05, 18N40 (Primary), 05E45 (Secondary)

Theory and Applications of Categories, Vol. 41, 2024, No. 3, pp 71-85.

Published 2024-01-23.

http://www.tac.mta.ca/tac/volumes/41/3/41-03.pdf

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