The Euler characteristic of a category


Venue   Category Theory 2006, White Point, Nova Scotia, 29/6/06

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.

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