(Op)lax natural transformations, twisted quantum field theories, and “even higher” Morita categories

Theo Johnson-Freyd, Claudia Scheimbauer

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

Motivated by the challenge of defining twisted quantum field theories in the context of higher categories, we develop a general framework for lax and oplax transformations and their higher analogs between strong (∞,n)-functors. We construct a double (∞,n)-category built out of the target (∞,n)-category governing the desired diagrammatics. We define (op)lax transformations as functors into parts thereof, and an (op)lax twisted field theory to be a symmetric monoidal (op)lax natural transformation between field theories. We verify that lax trivially-twisted relative field theories are the same as absolute field theories. As a second application, we extend the higher Morita category of Ed-algebras in a symmetric monoidal (∞,n)-category C to an (∞,n+d)-category using the higher morphisms in C.

Original languageEnglish
Pages (from-to)147-223
Number of pages77
JournalAdvances in Mathematics
Volume307
DOIs
StatePublished - 5 Feb 2017
Externally publishedYes

Keywords

  • Extended TFTs
  • Higher category theory

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