51 citations · 313 across the 22 of their papers we have counts for
22 papers
The microscopic weighting on a metric space
Emily Roff, Simon Willerton
We introduce the microscopic weighting, a canonical signed measure of mass one that can be associated to almost any finite metric space. The microscopic weighting is obtained as th…
Extranatural transformations, adjunctions of two variables and conjugation
Simon Willerton
Adjunctions of two variables generalize the relationship between tensor product and the internal hom functor in a closed monoidal category. For a pair of ordinary adjunctions $(F\d…
Metric-like spaces as enriched categories: three vignettes
Simon Willerton
This is a write-up of a talk given at the CATMI meeting in Bergen in July 2023, and is an introduction to a category-theoretic perspective on metric spaces. A metric space is a set…
On the magnitude of odd balls via potential functions
Simon Willerton
Magnitude is a measure of size defined for certain classes of metric spaces; it arose from ideas in category theory. In particular, magnitude is defined for compact subsets of Eucl…
The magnitude of odd balls via Hankel determinants of reverse Bessel polynomials
Simon Willerton
Magnitude is an invariant of metric spaces with origins in category theory. Using potential theoretic methods, Barceló and Carbery gave an algorithm for calculating the magnitude o…
Categorifying the magnitude of a graph
Richard Hepworth, Simon Willerton
The magnitude of a graph can be thought of as an integer power series associated to a graph; Leinster introduced it using his idea of magnitude of a metric space. Here we introduce…