#### Volume 8, issue 1 (2008)

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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