Lambda-presentable morphisms, injectivity and (weak) factorization systems

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dc.creatorHebert, Michel
dc.date2005-09-14
dc.date.accessioned2026-07-07T07:38:12Z
dc.date.available2026-07-07T07:38:12Z
dc.descriptionWe show that in a locally lambda-presentable category, every lambda(m)-injectivity class (i.e., the class of all the objects injective with respect to some class of lambda-presentable morphisms) is a weakly reflective subcategory determined by a functorial weak factorization system cofibrantly generated by a class of lambda-presentable morphisms. This was known for small-injectivity classes, and referred to as the "small object argument". An analogous result is obtained for orthogonality classes and factorization systems, where lambda-filtered colimits play the role of the transfinite compositions in the injectivity case. Lambda-presentable morphisms are also used to organize and clarify some related results (and their proofs), in particular on the existence of enough injectives (resp. pure-injectives).
dc.description16 pages
dc.identifierhttps://arxiv.org/abs/math/0509318
dc.identifierhttp://arxiv.org/abs/math/0509318
dc.identifierApplied Categorical Structures 14 (2006) 273-286 (http://springerlink.metapress.com/content/1572-9095/)
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/121037
dc.subjectCategory Theory
dc.subject18A20; 18A32
dc.titleLambda-presentable morphisms, injectivity and (weak) factorization systems
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