The smash product for derived categories in stable homotopy theory
Abstract
An E1 (or A-infinity) ring spectrum R has a derived category of modules DR. An E2 structure on R endows DR with a monoidal product. An E3 structure on R endows the monoidal product with a braiding. If the E3 structure extends to an E4 structure then the braided monoidal product is symmetric monoidal.
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