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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.date.accessioned2013-12-04T12:58:02Z
dc.date.created2010
dc.date.issued2010
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.identifier.issn0022-4049
dc.identifier.urihttp://hdl.handle.net/2117/20911
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.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.lcshAlgebra, Homological
dc.titleA Cartan-Eilenberg approach to homotopical algebra
dc.typeArticle
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
drac.iddocument12332182
dc.description.versionPostprint (published version)
dc.date.lift10000-01-01
upcommons.citation.authorGuillén, F.; Navarro, V.; Pascual, P.; Roig, A.
upcommons.citation.publishedtrue
upcommons.citation.publicationNameJournal of pure and applied algebra
upcommons.citation.volume214
upcommons.citation.startingPage140
upcommons.citation.endingPage164


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