Volume 8, issue 1 (2008)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Representations of spaces

Wojciech Chachólski and Jerome Scherer

Algebraic & Geometric Topology 8 (2008) 245–278
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