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.

Full text: dvi.gz 66 k, dvi 155 k, ps.gz 616 k, pdf 279 k.

Home Page of DOCUMENTA MATHEMATICA