## Abstract

Homotopical localizations with respect to a set of maps are known to exist in cofibrantly generated model categories (satisfying additional assumptions) [4, 13, 24, 35]. In this paper we expand the existing framework, so that it will apply to not necessarily cofibrantly generated model categories and, more important, will allow for a localization with respect to a class of maps (satisfying some restrictive conditions). We illustrate our technique by applying it to the equivariant model category of diagrams of spaces [12]. This model category is not cofibrantly generated [8]. We give conditions on a class of maps which ensure the existence of the localization functor; these conditions are satisfied by any set of maps and by the classes of maps which induce ordinary localizations on the generalized fixed-points sets.

Original language | English |
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Pages (from-to) | 93-139 |

Number of pages | 47 |

Journal | Israel Journal of Mathematics |

Volume | 147 |

DOIs | |

State | Published - 2005 |

Externally published | Yes |

## ASJC Scopus subject areas

- General Mathematics