# Finiteness obstructions and Euler characteristics of categories

@article{Fiore2009FinitenessOA, title={Finiteness obstructions and Euler characteristics of categories}, author={Thomas M. Fiore and Wolfgang Luck and Roman Sauer}, journal={Advances in Mathematics}, year={2009}, volume={226}, pages={2371-2469} }

We introduce notions of finiteness obstruction, Euler characteristic, L2-Euler characteristic, and Mobius inversion for wide classes of categories. The finiteness obstruction of a category Γ of type (FPR) is a class in the projective class group K0(RΓ); the functorial Euler characteristic and functorial L2-Euler characteristic are respectively its RΓ-rank and L2-rank. We also extend the second author's K-theoretic Mobius inversion from finite categories to quasi-finite categories. Our main… Expand

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