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

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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.

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Authors and Affiliations

  1. Einstein Institute of Mathematics, Edmond Safra Campus Givat Ram, The Hebrew University of Jerusalem, 91904, Jerusalem, Israel

    Boris Chorny

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  1. Boris Chorny
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Correspondence to Boris Chorny.

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During the preparation of this paper the author was a fellow of Marie Curie Training Site hosted by Centre de Recerca Matemàtica (Barcelona), grant no. HPMT-CT-2000-00075 of the European Commission.

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Chorny, B. Localization with respect to a class of maps I — Equivariant localization of diagrams of spaces. Isr. J. Math. 147, 93–139 (2005). https://doi.org/10.1007/BF02785361

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