The following paper is available. It is the full version of the talk I gave at CT06. "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 Mobius-Rota inversion from posets to categories. http://arxiv.org/abs/math.CT/0610260 Best wishes, Tom -- Tom Leinster <tl@maths.gla.ac.uk>