Geodesic
The category of necklaces is Reedy monoidal
Theory and applications of categories, Tome 41 (2024), pp. 71-85

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.

Classification : 18M05, 18N40 (Primary), 05E45 (Secondary)
Keywords: Reedy category, necklaces, monoidal model category 
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     author = {Violeta Borges Marques and Arne Mertens},
     title = {The category of necklaces is {Reedy} monoidal},
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     pages = {71--85},
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     volume = {41},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a2/}
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Violeta Borges Marques; Arne Mertens. The category of necklaces is Reedy monoidal. Theory and applications of categories, Tome 41 (2024), pp. 71-85. http://geodesic.mathdoc.fr/item/TAC_2024_41_a2/