TY - JOUR
T1 - (Op)lax natural transformations, twisted quantum field theories, and “even higher” Morita categories
AU - Johnson-Freyd, Theo
AU - Scheimbauer, Claudia
N1 - Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2017/2/5
Y1 - 2017/2/5
N2 - 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.
AB - 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.
KW - Extended TFTs
KW - Higher category theory
UR - http://www.scopus.com/inward/record.url?scp=84997541927&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2016.11.014
DO - 10.1016/j.aim.2016.11.014
M3 - Article
AN - SCOPUS:84997541927
SN - 0001-8708
VL - 307
SP - 147
EP - 223
JO - Advances in Mathematics
JF - Advances in Mathematics
ER -