The category of necklaces is Reedy monoidal

2023/08/24 by Marques, Violeta Borges, Mertens, Arne
#05E45 (Secondary) #18M05 #18N40 (Primary) #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.12796

Abstract

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 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.

Related

• Reedy diagrams in symmetric monoidal model categories
• Enriched Reedy categories
• Monoidal categories in, and linking, geometry and algebra
• Colax Reedy diagrams
• Monoidal model categories