The Euler characteristic of a category as the sum of a divergent series

2007/07/05 by Tom Leinster, Leinster, Tom · 1 citation
Mathematics · #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #math.AT #math.CT

paper · pdf · doi:10.48550/arxiv.0707.0835

11 pages

arxiv created 2007/07/05 · arxiv updated 2009/12/01

Abstract

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 (math.CT/0610260).

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