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

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Classification : 18G80, 18F25, 19D23, 18M65
Keywords: Tensor triangulated category, determinant functor, multicategory, Picard groupoid, categorical ring, K-Theory, cubical complex 
@article{TAC_2023_39_a26,
     author = {Ettore Aldrovandi and Cynthia Lester},
     title = {On {Multi-Determinant} {Functors} for {Triangulated} {Categories}},
     journal = {Theory and applications of categories},
     pages = {769--803},
     year = {2023},
     volume = {39},
     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/