Representations of spaces

Chachólski, Wojciech¹ ; Scherer, Jerome²

¹K.T.H., Matematik, S-10044 Stockholm, Sweden
²Universitat Autònoma de Barcelona, Departament de Matemàtiques, E-08193 Bellaterra, Spain

Algebraic and Geometric Topology, Tome 8 (2008) no. 1, pp. 245-278

Résumé

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.

Détail

DOI : 10.2140/agt.2008.8.245

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

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