Comparing homotopy categories

Publisher： Cambridge University Press

E-ISSN： 1865-5394|2|1|169-205

ISSN： 1865-2433

Source： Journal of K-Theory, Vol.2, Iss.1, 2008-08, pp. : 169-205

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Abstract

Given a suitable functor T : → between model categories, we define a long exact sequence relating the homotopy groups of any X ε with those of TX, and use this to describe an obstruction theory for lifting an object G ε to . Examples include finding spaces with given homology or homotopy groups.

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