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SUMMARY:(Op)lax natural transformations for higher categories\, relative q
uantum field theories\, and the "even higher" Morita category
DTSTART;VALUE=DATE-TIME:20151023T094000Z
DTEND;VALUE=DATE-TIME:20151023T103000Z
DTSTAMP;VALUE=DATE-TIME:20201025T060328Z
UID:indico-contribution-2610@indico.math.cnrs.fr
DESCRIPTION:Speakers: Claudia Scheimbauer (Max Planck Institute for Mathem
atics\, Bonn)\nA relative (also called twisted) quantum field theory shoul
d be some transformation between quantum field theories\, which themselves
are symmetric monoidal functors out of a space-time category. In examples
\, the notion of natural transformation turns out to be too strong\, makin
g it necessary to relax it. In joint work with Theo Johson-Freyd we provid
e a framework for both lax and oplax transformations and their higher anal
ogs\, known as transfors\, between strong $(\\infty\, n)$-functors. It is
given by a double $(\\infty\,n)$-category built out of the target $(\\inf
ty\, n)$-category that we call its (op)lax square\, which governs the desi
red diagrammatics. Lax or oplax transfors then are functors into parts of
the oplax square. Finally\, I will explain how to use the (op)lax square
to extend the construction of the higher Morita category of $E_d$-algebras
in an $(\\infty\,n)$-category $\\mathcal C$ to an even higher level using
the higher morphisms of $\\mathcal C$.\n\nhttps://indico.math.cnrs.fr/eve
nt/807/contributions/2610/
LOCATION:Institut de MathÃ©matiques de Toulouse Amphi Schwartz\, bat. 1R3
URL:https://indico.math.cnrs.fr/event/807/contributions/2610/
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