On Multi-Determinant Functors for Triangulated Categories
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2023
- DOI:
- 10.48550/arXiv.2305.02293
- arXiv:
- arXiv:2305.02293
- Bibcode:
- 2023arXiv230502293A
- Keywords:
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- Mathematics - Category Theory;
- Mathematics - Algebraic Topology;
- Mathematics - K-Theory and Homology
- E-Print:
- 35 Pages. Added a few clarifying sentences at the referee's request. No substantial changes. Version accepted by Theory and Applications of Categories