THE EULER CHARACTERISTIC OF A CATEGORY AS THE SUM OF A DIVERGENT SERIES

By Tom Leinster. 2007

49 citations recorded by the source corpus.

The Euler characteristic of a cell complex is often thought of as the alternating sum of the number of cells of each dimension. When the complex is infinite, the sum diverges. Nevertheless, it can sometimes be evaluated; in particular, this is possible when the complex is the nerve of a finite category. This provides an alternative definition of the Euler characteristic of a category, which is in many cases equivalent to the original one.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7499642ab13ca3175b6e971febcba566c7e1f194

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Magnitude homology of enriched categories and metric spaces (2017, result): “groups, not homology groups. Moreover, although one can sum the divergent series of Theorem 6.29 in more generality to deﬁne a more general notion of “series magnitude” for enriched categories, as in [BL08], the result is no longer invariant under equivalence of categories. We can however extend the”
The magnitude of metric spaces (2010, methodology): “Already, several cardinality-like invariants are tied together by the notion of the Euler characteristic of a category [17, 3].”
On the asymptotic magnitude of subsets of Euclidean space (2009, background): “In the first part of this section a metric space is viewed as an enriched category so that the magnitude can be defined analogously to the Euler characteristic of a finite category which was introduced in [7] and [1].”