Geodesic
The Euler characteristic of a category
Documenta mathematica, Tome 13 (2008), pp. 21-49.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 18F99, 55U99, 05C50, 57N65
Keywords: Euler characteristic, finite category, inclusion-exclusion, Möbius inversion, cardinality of colimit 
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Leinster, Tom. The Euler characteristic of a category. Documenta mathematica, Tome 13 (2008), pp. 21-49. http://geodesic.mathdoc.fr/item/DOCMA_2008__13__a22/