Category Theory 2018, University of Azores, 13 July 2018
Magnitude is a numerical invariant of enriched categories. It unifies many
invariants of size from across mathematics, including cardinality, volume,
dimension and Euler characteristic. The study of magnitude has spread out
in unexpected directions:
As well as giving an overview of all this, I will take some time to discuss
the role of category theory in the development and which parts (to bend a
phrase of Lawvere) come from "taking enriched categories seriously".
theorems on the geometric content of magnitude have called upon some very
sophisticated analysis (Barceló, Carbery, Gimperlein, Goffeng, Meckes);
magnitude was the springboard for a newly rigorous and systematic theory of
diversity, particularly applicable in biological settings (Cobbold, Meckes);
magnitude has now been categorified to a theory of magnitude homology; thus,
magnitude homology is to magnitude as topological homology is to Euler
characteristic (Hepworth, Shulman, Willerton).
In this pdf file.
See this bibliography
for references and further reading.
This page was last changed on 5 May 2019.