Homology, Homotopy and Applications

Volume 6 (2004)

Number 1

Homology fibrations and “group-completion” revisited

Pages: 153 – 166

DOI: http://dx.doi.org/10.4310/HHA.2004.v6.n1.a10


Wolfgang Pitsch (Institut de Mathématiques, Université de Genève, Switzerland)

Jérôme Scherer (Departament de Matemátiques, Universitat Autònoma de Barcelona, Bellaterra, Spain)


We give a proof of the Jardine-Tillmann generalized group completion theorem. It is much in the spirit of the original homology fibration approach by McDuff and Segal, but follows a modern treatment of homotopy colimits, using as little simplicial technology as possible. We compare simplicial and topological definitions of homology fibrations.


group completion, homology fibration, plus-construction, barycentric subdivision, simplex category

2010 Mathematics Subject Classification

Primary 55U10. Secondary 19D06.

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