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