Venue   Category Theory 2018, University of Azores, 13 July 2018

Abstract   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:

  • 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).
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".

Slides   In this pdf file. See this bibliography for references and further reading.

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