The Euler characteristic of a category

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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 is proved for the cardinality of a colimit of sets, generalizing the classical inclusion-exclusion formula. Both rest on a generalization of Rota's Mobius inversion from posets to categories.

Original languageEnglish
Pages (from-to)21-49
Number of pages29
JournalDocumenta mathematica
Volume13
Publication statusPublished - 2008

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