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.
Cite
@article{arxiv.2305.02293,
title = {On Multi-Determinant Functors for Triangulated Categories},
author = {Ettore Aldrovandi and Cynthia Lester},
journal= {arXiv preprint arXiv:2305.02293},
year = {2023}
}
Comments
35 Pages. Added a few clarifying sentences at the referee's request. No substantial changes. Version accepted by Theory and Applications of Categories