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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