## Localization with respect to a class of maps I – Equivariant localization of diagrams of spaces

Citations: | 4 - 4 self |

### BibTeX

@TECHREPORT{Chorny_localizationwith,

author = {Boris Chorny},

title = {Localization with respect to a class of maps I – Equivariant localization of diagrams of spaces},

institution = {},

year = {}

}

### OpenURL

### Abstract

Abstract. Homotopical localizations with respect to a set of maps are known to exist in cofibrantly generated model categories (satisfying additional assumptions) [3, 12, 20, 29]. 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 [11]. This model category is not cofibrantly generated [7]. 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 class of maps which induces ordinary localizations on the generalized fixed-points sets.