Open Access
2017 The higher Morita category of $\mathbb{E}_{n}$–algebras
Rune Haugseng
Geom. Topol. 21(3): 1631-1730 (2017). DOI: 10.2140/gt.2017.21.1631

Abstract

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

Citation

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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

Information

Received: 18 February 2015; Revised: 7 April 2016; Accepted: 8 May 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06726510
MathSciNet: MR3650080
Digital Object Identifier: 10.2140/gt.2017.21.1631

Subjects:
Primary: 18D50 , 55U35
Secondary: 16D20

Keywords: \mathbbE_n–algebras , higher Morita category , iterated bimodules

Rights: Copyright © 2017 Mathematical Sciences Publishers

Vol.21 • No. 3 • 2017
MSP
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