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

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

2007-07-05

arxiv.org/abs/0707.0835v1

Mathematics

Category Theory

11 pages

Scientific paper

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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