### 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. © 2008 Algebraic & Geometric Topology.

Original language | English |
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Pages (from-to) | 245-278 |

Journal | Algebraic and Geometric Topology |

Volume | 8 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Dec 2008 |

### Keywords

- Action of spaces
- Mapping space
- Model approximation
- Model category
- Monoidal category
- Monoidal model category

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## Cite this

Chachólski, W., & Scherer, J. (2008). Representations of spaces.

*Algebraic and Geometric Topology*,*8*(1), 245-278. https://doi.org/10.2140/agt.2008.8.245