#
Tensor-triangulated categories and dualities

##
Baptiste Calmès and Jens Hornbostel

In a triangulated closed symmetric monoidal category, there are natural
dualities induced by the internal Hom. Given a monoidal exact functor
$f^*$ between two such categories and adjoint couples $(f^*,f_*)$,
$(f_*,f^!)$, we establish the commutative diagrams necessary for $f^*$ and
$f_*$ to respect certain dualities, for a projection formula to hold
between them (as duality preserving exact functors) and for classical base
change and composition formulas to hold when such duality preserving
functors are composed. This framework allows us to define push-forwards
for Witt groups, for example.

Keywords:
closed monoidal category, commutative diagram, duality, Witt group

2000 MSC:
18D10

*Theory and Applications of Categories,*
Vol. 22, 2009,
No. 6, pp 136-198.

http://www.tac.mta.ca/tac/volumes/22/6/22-06.dvi

http://www.tac.mta.ca/tac/volumes/22/6/22-06.ps

http://www.tac.mta.ca/tac/volumes/22/6/22-06.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/6/22-06.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/6/22-06.ps

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