Homology, Homotopy and Applications

Volume 19 (2017)

Number 1

Čech complexes for covers of small categories

Pages: 281 – 291

DOI: https://dx.doi.org/10.4310/HHA.2017.v19.n1.a14


Kohei Tanaka (Institute of Social Sciences, Shinshu University, Matsumoto, Nagano, Japan)


We present a combinatorial analogue of the nerve theorem for covers of small categories, using the Grothendieck construction. We apply our result to prove the inclusion-exclusion principle for the Euler characteristic of a finite category.


nerve theorem, small category, inclusion-exclusion principle, Euler characteristic

2010 Mathematics Subject Classification

46M20, 55P10

Published 6 June 2017