Ring operads and symmetric bimonoidal categories (2409.09664v1)

Abstract: We generalize the classical operad pair theory to a new model for $E_\infty$ ring spaces, which we call ring operad theory, and establish a connection with the classical operad pair theory, allowing the classical multiplicative infinite loop machine to be applied to algebras over any $E_\infty$ ring operad. As an application, we show that classifying spaces of symmetric bimonoidal categories are directly homeomorphic to certain $E_\infty$ ring spaces in the ring operad sense. Consequently, this provides an alternative construction from symmetric bimonoidal categories to classical $E_\infty$ ring spaces. We also present a comparison between this construction and the classical approach.