The higher Morita category of E-n-algebras

摘要

We introduce simple models for associative algebras and bimodules in the context of nonsymmetric infinity-operads, and use these to construct an (infinity, 2)-category of associative algebras, bimodules and bimodule homomorphisms in a monoidal infinity-category. By working with infinity-operads over Delta(n,op) we iterate these definitions and generalize our construction to get an(infinity, n+1)-category of E-n-algebras and iterated bimodules in an E-n-monoidal infinity-category. Moreover, we show that if C is an En+k-monoidal infinity-category then the (infinity, n+1)-category of E-n-algebras in C has a natural E-k-monoidal structure. We also identify the mapping (infinity, n)-categories between two E-n-algebras, which allows us to define interesting nonconnective deloopings of the Brauer space of a commutative ring spectrum.