Ring operads and symmetric bimonoidal categories

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.

42 pages