Abstract
We introduce simple models for associative algebras and bimodules in the context of nonsymmetric –operads, and use these to construct an –category of associative algebras, bimodules and bimodule homomorphisms in a monoidal –category. By working with –operads over we iterate these definitions and generalize our construction to get an –category of –algebras and iterated bimodules in an –monoidal –category. Moreover, we show that if is an –monoidal –category then the –category of –algebras in has a natural –monoidal structure. We also identify the mapping –categories between two –algebras, which allows us to define interesting nonconnective deloopings of the Brauer space of a commutative ring spectrum.
Citation
Rune Haugseng. "The higher Morita category of $\mathbb{E}_{n}$–algebras." Geom. Topol. 21 (3) 1631 - 1730, 2017. https://doi.org/10.2140/gt.2017.21.1631
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