The Euler characteristic of a category

Tom Leinster

Type: Article

Publication Date: 2008-01-01

Citations: 118

DOI: https://doi.org/10.4171/dm/240

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 Möbius inversion from posets to categories.

Locations

Documenta Mathematica - View - PDF
arXiv (Cornell University) - View - PDF

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Works Cited by This (30)

Action	Title	Year	Authors
+	Mobius Functions, Incidence Algebras and Power Series Representations	1986	Arne Dür
+	Introduction to geometric probability	1998	Gian‐Carlo Rota
+	Combinatorial Species and Tree-like Structures	1997	François Bergeron Gilbert Labelle Pierre Leroux
+	Taking categories seriously	1986	F. William Lawvere
+	A general theory of self-similarity II: recognition	2004	Tom Leinster
+	Euler measure as generalized cardinality	2002	James Propp
+	From Finite Sets to Feynman Diagrams	2001	John C. Baez James G. Dolan
+	A classification of accessible categories	2002	Jiřı́ Adámek Francis Borceux Stephen Lack Jiřı́ Rosický
+	Euler characteristics and characters of discrete groups	1976	Hyman Bass
+	Categories of continuous functors, I	1972	Peter Freyd G. M. Kelly