En-ring categories Original Research Article

We show that a category A with a coherent ring structure determines a ring spectrum imageA whose zeroth space is an additive group completion of the classifying space BA. This contains Mayʹs result that a bipermutative category determines an E∞ ring spectrum. It also implies that a braided bimonoidal category determines an E2 ring spectrum. If X is an En-space, we also construct a ring category A whose associated ring spectrum imageA is the En ring spectrum QX +, the stable homotopy of X−.