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 Hepworth--Willerton magnitude homology of graphs, and detects geometric information such as convexity.
Original language | English |
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Pages (from-to) | 2175-2221 |
Number of pages | 35 |
Journal | Algebraic and Geometric Topology |
Volume | 21 |
Issue number | 5 |
DOIs | |
Publication status | Published - 29 Nov 2021 |