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The category of necklaces is Reedy monoidal

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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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