ar X iv : m at h / 05 09 31 8 v 1 [ m at h . C T ] 1 4 Se p 20 05 λ - PRESENTABLE MORPHISMS , INJECTIVITY AND ( WEAK ) FACTORIZATION SYSTEMS
نویسنده
چکیده
We show that every λm-injectivity class (i.e., the class of all the objects injective with respect to some class of λ-presentable morphisms) is a weakly reflective subcategory determined by a functorial weak factorization system cofibrantly generated by a class of λ-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 λ-filtered colimits play the role of the transfinite compositions in the injectivity case. λ-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).
منابع مشابه
Algebraically Closed and Existentially Closed Substructures in Categorical Context
We investigate categorical versions of algebraically closed (= pure) embeddings, existentially closed embeddings, and the like, in the context of locally presentable categories. The definitions of S. Fakir [Fa, 75], as well as some of his results, are revisited and extended. Related preservation theorems are obtained, and a new proof of the main result of Rosický, Adámek and Borceux ([RAB, 02])...
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