Homology, Homotopy and Applications

Volume 7 (2005)

Number 1

What does the classifying space of a category classify?

Pages: 185 – 195

DOI: https://dx.doi.org/10.4310/HHA.2005.v7.n1.a10


Michael Weiss (Department of Mathematics, University of Aberdeen, Scotland, United Kingdom)


The classifying space of a small category classifies sheaves whose values are contravariant functors from that category to sets and whose stalks are representable.


category, classifying space, sheaf, representable functor

2010 Mathematics Subject Classification

18F20, 18G55, 57T30

Published 1 January 2005