Representations of spaces

Chachólski, Wojciech; Scherer, Jerome

doi:10.2140/agt.2008.8.245

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Representations of spaces

Wojciech Chachólski and Jerome Scherer

Algebraic & Geometric Topology 8 (2008) 245–278

DOI: 10.2140/agt.2008.8.245

Abstract

We explain how the notion of homotopy colimits gives rise to that of mapping spaces, even in categories which are not simplicial. We apply the technique of model approximations and use elementary properties of the category of spaces to be able to construct resolutions. We prove that the homotopy category of any monoidal model category is always a central algebra over the homotopy category of $Spaces$ .

Keywords

model category, model approximation, mapping space, action of spaces, monoidal category, monoidal model category

Mathematical Subject Classification 2000

Primary: 55U35, 18G55

Secondary: 18G10

References

Publication

Received: 5 September 2007

Revised: 19 December 2007

Accepted: 19 December 2007

Published: 12 March 2008

Authors

Wojciech Chachólski
K.T.H. Matematik S-10044 Stockholm Sweden

Jerome Scherer
Universitat Autònoma de Barcelona Departament de Matemàtiques E-08193 Bellaterra Spain

Volume 8, issue 1 (2008)