Duals and adjoints in higher Morita categories

2018/04/29 by Gwilliam, Owen, Scheimbauer, Claudia · 2 citations
#Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1804.10924

Abstract

We study duals for objects and adjoints for k-morphisms in Alg_n(S), an (∞,n+N)-category that models a higher Morita category for E_n algebra objects in a symmetric monoidal (∞,N)-category S. Our model of Alg(S) uses the geometrically convenient framework of factorization algebras. The main result is that Alg_n(S) is fully n-dualizable, verifying a conjecture of Lurie. Moreover, we unpack the consequences for a natural class of fully extended topological field theories and explore (n+1)-dualizability.

Cited by

• The Morita (∞,2)-category of a monoidal category as a 2-complicial set
• Relative Invertibility and Full Dualizability of Finite Braided Tensor Categories

Related

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• Some remarks on higher Morita categories
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• Morita theory in enriched context
• Koszul duality between E_n-algebras and coalgebras in a filtered category