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dc.contributor.authorGuillén Santos, Francisco
dc.contributor.authorNavarro Aznar, Vicente
dc.contributor.authorPascual Gainza, Pere
dc.contributor.authorRoig Martí, Agustín
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I
dc.identifier.citationGuillén, F. [et al.]. A Cartan-Eilenberg approach to homotopical algebra. "Journal of pure and applied algebra", 2010, vol. 214, p. 140-164.
dc.description.abstractIn this paper we propose an approach to homotopical algebra w here the basic ingredient is a category with two classes of distinguished morphisms: s trong and weak equivalences. These data determine the cofibrant objects by an extension property ana logous to the classical lifting property of projective modules. We define a Cartan-Eilenberg categor y as a category with strong and weak equivalences such that there is an equivalence of categorie s between its localisation with respect to weak equivalences and the relative localisation of the subc ategory of cofibrant objets with respect to strong equivalences. This equivalence of categories allow s us to extend the classical theory of derived additive functors to this non additive setting. The main exa mples include Quillen model categories and categories of functors defined on a category endowed with a cotriple (comonad) and taking values on a category of complexes of an abelian category. In the latt er case there are examples in which the class of strong equivalences is not determined by a homotopy relation. Among other applications of our theory, we establish a very general acyclic models theor em
dc.format.extent25 p.
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshAlgebra, Homological
dc.titleA Cartan-Eilenberg approach to homotopical algebra
dc.subject.lemacÀlgebra homològica
dc.contributor.groupUniversitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
dc.description.peerreviewedPeer Reviewed
dc.rights.accessRestricted access - publisher's policy
dc.description.versionPostprint (published version)
upcommons.citation.authorGuillén, F.; Navarro, V.; Pascual, P.; Roig, A.
upcommons.citation.publicationNameJournal of pure and applied algebra

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