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Applied Categorical Structures

, Volume 18, Issue 4, pp 343–375 | Cite as

Exact Sequences and Closed Model Categories

  • Mónica García Pinillos
  • Luis Javier Hernández Paricio
  • María Teresa Rivas Rodríguez
Article

Abstract

For every closed model category with zero object, Quillen gave the construction of Eckman-Hilton and Puppe sequences. In this paper, we remove the hypothesis of the existence of zero object and construct (using the category over the initial object or the category under the final object) these sequences for unpointed model categories. We illustrate the power of this result in abstract homotopy theory given some interesting applications to group cohomology and exterior homotopy groups.

Keywords

Quillen model category Model category with non-zero object Fibration sequence Cofibration sequence Group cohomology Brown-Grossman homotopy group Steenrod homotopy group Exterior space Proper homotopy Shape theory 

Mathematics Subject Classifications (2000)

55U35 55U40 55N25 55Q70 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Mónica García Pinillos
    • 1
  • Luis Javier Hernández Paricio
    • 1
  • María Teresa Rivas Rodríguez
    • 1
  1. 1.Departamento de MatemáticasUniversidad de La RiojaLogroñoSpain

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