The 2-monoidal structure of symmetric sequences

Abstract

We prove a conjecture proposed by Dwyer and Hess (2014), namely that the category of symmetric sequences, when equipped with the composition and matrix monoidal structures, forms a 2-monoidal category in the sense of Aguiar and Mahajan (2010). Our approach leverages a detailed analysis of the interplay between these two monoidal structures, offering new insights into their behavior. As a consequence, we are able to show that every operad admits a Day-operad structure.