Magnitude homology of enriched categories and metric spaces

Tom Leinster, Michael Shulman

Research output: Contribution to journalArticlepeer-review


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 Hepworth--Willerton magnitude homology of graphs, and detects geometric information such as convexity.
Original languageEnglish
Number of pages35
JournalAlgebraic and Geometric Topology
Publication statusAccepted/In press - 12 Nov 2020


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