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arXiv · 1711.00802

Magnitude homology of enriched categories and metric spaces

Tom Leinster·Michael Shulman
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Abstract

Magnitude is a numerical invariant of enriched categories, including in particular metric spaces as $[0,\infty)$-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.

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Tom Leinster, Michael Shulman. 2020-11-15. Magnitude homology of enriched categories and metric spaces. https://doi.org/10.2140/agt.2021.21.2175

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