caa a22 4500 467882754 CHVBK 20180406152724.0 cr unu---uuuuu 170328e20060801xx s 000 0 eng 10.1007/s10485-006-9024-9 doi (NATIONALLICENCE)springer-10.1007/s10485-006-9024-9 Hébert Michel Department of Mathematics, The American University in Cairo, Box 2511, Cairo, Egypt aut $\lambda$ -presentable Morphisms, Injectivity and (Weak) Factorization Systems [Elektronische Daten] [Michel Hébert] We 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). Finally, locally $\lambda$ -presentable categories are shown to be cellularly generated by the set of morphisms between $\lambda$ -presentable objects. Springer Science + Business Media B.V., 2006 Applied Categorical Structures Kluwer Academic Publishers 14/4(2006-08-01), 273-289 0927-2852 14:4<273 2006 14 10485 https://doi.org/10.1007/s10485-006-9024-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10485-006-9024-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Hébert Michel Department of Mathematics, The American University in Cairo, Box 2511, Cairo, Egypt aut NATIONALLICENCE 773 0- Applied Categorical Structures Kluwer Academic Publishers 14/4(2006-08-01), 273-289 0927-2852 14:4<273 2006 14 10485 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer