3 papers
math.MG2026
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…
math.CT2025
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…
math.CT2024
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…