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The Euler characteristic of a category

Tom Leinster
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Abstract

The Euler characteristic of a finite category is defined and shown to be compatible with Euler characteristics of other types of object, including orbifolds. A formula for the cardinality of the colimit of a diagram of sets is proved, generalizing the classical inclusion-exclusion formula. Both rest on a generalization of Mobius-Rota inversion from posets to categories.

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Tom Leinster. 2006-10-08. The Euler characteristic of a category. https://arxiv.org/abs/math/0610260

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