arXiv subjects

Cynthia Lester

Publications and source records attributed to Cynthia Lester.

3 recordsLinked to original sources

arXiv2023

On Multi-Determinant Functors for Triangulated Categories

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.

math.CT↗

arXiv2019

Covers in the Canonical Grothendieck Topology

We explore the canonical Grothendieck topology in some specific circumstances. First we use a description of the canonical topology to get a variant of Giraud's Theorem. Then we explore the canonical Grothendieck topology on the categories of sets and topological spaces; here we get a nice basis for the topology. Lastly, we look at the canonical Grothendieck topology on the category of $R$-modules.

math.AT↗

arXiv2019

The Canonical Grothendieck Topology and a Homotopical Analog

We explore the canonical Grothendieck topology and a new homotopical analog. First we discuss some background information, including defining a new 2-category called the Index-Functor Category and a sieve generalization. Then we discuss a specific description of the covers in the canonical topology and a homotopical analog. Lastly, we explore the covers in the homotopical analog by obtaining some examples.

math.AT↗