White Point, Nova Scotia,
Abstract Many types of mathematical object, beyond 'well-behaved' topological spaces, can be assigned an Euler characteristic in a sensible and useful way. This applies, in particular, to categories. To define the Euler characteristic of a category, I will use a construction that generalizes both the Möbius inversion formula of number theory and the inclusion-exclusion principle of combinatorics. I will explain why it deserves to be called Euler characteristic, and how it relates to Euler characteristics of other types of object. This builds on work of Rota, Schanuel, Baez, Dolan, and others.
Slides In this pdf file (2.9MB).
Errata Page 2: 'Leray' should be 'Lemay'. Page 3: DN should have objects 0, ..., N. Page 9: the monoid M should be a group.