DOCUMENTA MATHEMATICA, Vol. 13 (2008), 21-49

Tom Leinster

The Euler Characteristic of a Category

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 Möbius inversion from posets to categories.

2000 Mathematics Subject Classification: 18F99, 55U99, 05C50, 57N65.

Keywords and Phrases: Euler characteristic, finite category, inclusion-exclusion, Möbius inversion, cardinality of colimit.

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