Natural weak factorization systems
Grandis, Marco ; Tholen, Walter
Archivum Mathematicum, Tome 042 (2006), p. 397-408 / Harvested from Czech Digital Mathematics Library
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In order to facilitate a natural choice for morphisms created by the (left or right) lifting property as used in the definition of weak factorization systems, the notion of natural weak factorization system in the category $\mathcal {K}$ is introduced, as a pair (comonad, monad) over $\mathcal {K}^{\bf 2}$. The link with existing notions in terms of morphism classes is given via the respective Eilenberg–Moore categories.

Publié le : 2006-01-01
Classification:  18C15 
@article{108015,
     author = {Marco Grandis and Walter Tholen},
     title = {Natural weak factorization systems},
     journal = {Archivum Mathematicum},
     volume = {042},
     year = {2006},
     pages = {397-408},
     zbl = {1164.18300},
     mrnumber = {2283020},
     language = {en},
     url = {http://dml.mathdoc.fr/item/108015}
}

Grandis, Marco; Tholen, Walter. Natural weak factorization systems. Archivum Mathematicum, Tome 042 (2006) pp. 397-408. http://gdmltest.u-ga.fr/item/108015/

Adámek J.; Herrlich H.; Rosický J.; Tholen W. Weak factorization systems and topological functors, Appl. Categorical Structures 10 (2002), 237–249. | MR 1916156 | Zbl 0997.18002

Adámek J.; Herrlich H.; Strecker G. E. Abstract and Concrete Categories, Wiley (New York 1990). (1990) | MR 1051419

Carboni A.; Janelidze G. Decidable (= separable) objects and morphisms in lextensive categories, J. Pure Appl. Algebra 110 (1996), 219–240. (1996) | MR 1393114 | Zbl 0858.18004

Coppey L. Algèbres de decompositions et précatégories, Diagrammes 4 (Suppl.) (1980). (1980) | MR 0684912 | Zbl 0497.18015

Grandis M.; Paré R. Limits in double categories, Cah. Topol. Géom. Différ. Catég. 40 (1999), 162–220. (1999) | MR 1716779 | Zbl 0939.18007

Gray J. W. Formal category theory: adjointness for 2-categories, Lecture Notes in Math. Vol. 391, Springer-Verlag (Berlin 1974). (1974) | MR 0371990 | Zbl 0285.18006

Korostenski M.; Tholen W. Factorization systems as Eilenberg–Moore algebras, J. Pure Appl. Algebra 85 (1993), 57–72. (1993) | MR 1207068 | Zbl 0778.18001

Rosický J.; Tholen W. Lax factorization algebras, J. Pure Appl. Algebra 175 (2002), 355–382. | MR 1935984 | Zbl 1013.18001

Rosický J.; Tholen W. Factorization, fibration and torsion, preprint (York University 2006). | MR 2369170 | Zbl 1184.18009

Rosebrugh R.; Wood R. J. Coherence for factorization algebras, Theory Appl. Categories 10 (2002), 134–147. | MR 1883483 | Zbl 0994.18001