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

Primary: 18G55, 55U35

Secondary: 18G10

References

Publication

Received: 5 September 2007
Revised: 19 December 2007
Accepted: 19 December 2007
Published: 12 March 2008

Authors