Abstract / Description of output
Magnitude is a numerical invariant of enriched categories, including in particular metric spaces as [0,∞)enriched categories. We show that in many cases magnitude can be categorified to a homology theory for enriched categories, which we call magnitude homology (in fact, it is a special sort of Hochschild homology), whose graded Euler characteristic is the magnitude. Magnitude homology of metric spaces generalizes the HepworthWillerton magnitude homology of graphs, and detects geometric information such as convexity.
Original language  English 

Publisher  ArXiv 
Publication status  Published  15 Nov 2020 
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Tom Leinster
 School of Mathematics  Personal Chair of Category Theory
Person: Academic: Research Active