Geodesic
Several constructions for factorization systems
Theory and applications of categories, Tome 12 (2004), pp. 326-354.

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The paper develops the previously proposed approach to constructing factorization systems in general categories. This approach is applied to the problem of finding conditions under which a functor (not necessarily admitting a right adjoint) `reflects' factorization systems. In particular, a generalization of the well-known Cassidy-Héebert-Kelly factorization theorem is given. The problem of relating a factorization system to a pointed endofunctor is considered. Some relevant examples in concrete categories are given.
Classification : 18A20, 18A32, 18A25
Keywords: (local) factorization system, family of adjunctions between slice categories, semi-left-exact reflection, fibration, (co)pointed endofunctor 
@article{TAC_2004_12_a10,
     author = {Dali Zangurashvili},
     title = {Several constructions for factorization systems},
     journal = {Theory and applications of categories},
     pages = {326--354},
     publisher = {mathdoc},
     volume = {12},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2004_12_a10/}
}
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Dali Zangurashvili. Several constructions for factorization systems. Theory and applications of categories, Tome 12 (2004), pp. 326-354. http://geodesic.mathdoc.fr/item/TAC_2004_12_a10/