Homology, Homotopy and Applications

Volume 25 (2023)

Number 2

Classifying space via homotopy coherent nerve

Pages: 373 – 381

DOI: https://dx.doi.org/10.4310/HHA.2023.v25.n2.a16


Kensuke Arakawa (Department of Mathematics, Kyoto University, Kyoto, Japan)


We prove that the classifying space of a simplicial group is modeled by its homotopy coherent nerve. We will also show that the claim remains valid for simplicial groupoids.


classifying space, homotopy coherent nerve

2010 Mathematics Subject Classification

18D50, 55R35

Received 13 August 2022

Accepted 14 September 2022

Published 22 November 2023