Geodesic
Tensor-triangulated categories and dualities
Theory and applications of categories, Tome 22 (2009), pp. 136-198

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.

Classification : 18D10
Keywords: closed monoidal category, commutative diagram, duality, Witt group 
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     author = {Baptiste Calm\`es and Jens Hornbostel},
     title = {Tensor-triangulated categories and dualities},
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     pages = {136--198},
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     volume = {22},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2009_22_a5/}
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Baptiste Calmès; Jens Hornbostel. Tensor-triangulated categories and dualities. Theory and applications of categories, Tome 22 (2009), pp. 136-198. http://geodesic.mathdoc.fr/item/TAC_2009_22_a5/