Geodesic
On Multi-Determinant Functors for Triangulated Categories
Theory and applications of categories, Tome 39 (2023), pp. 769-803

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

We extend Deligne's notion of determinant functor to tensor triangulated categories. Specifically, to account for the multiexact structure of the tensor, we define a determinant functor on the 2-multicategory of triangulated categories and we provide a multicategorical version of the universal determinant functor for triangulated categories whose multiexactness properties are conveniently captured by a certain complex modeled by cubical shapes, which we introduce along the way. We then show that for a tensor triangulated category whose tensor admits a Verdier structure the resulting determinant functor takes values in a categorical ring.

Publié le :
Classification : 18G80, 18F25, 19D23, 18M65
Keywords: Tensor triangulated category, determinant functor, multicategory, Picard groupoid, categorical ring, K-Theory, cubical complex 
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     author = {Ettore Aldrovandi and Cynthia Lester},
     title = {On {Multi-Determinant} {Functors} for {Triangulated} {Categories}},
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     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2023_39_a26/}
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Ettore Aldrovandi; Cynthia Lester. On Multi-Determinant Functors for Triangulated Categories. Theory and applications of categories, Tome 39 (2023), pp. 769-803. http://geodesic.mathdoc.fr/item/TAC_2023_39_a26/