Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Summary:
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.
References:
[1] 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
[2] Adámek J., Herrlich H., Strecker G. E.: Abstract and Concrete Categories. Wiley (New York 1990). MR 1051419
[3] Carboni A., Janelidze G.: Decidable (= separable) objects and morphisms in lextensive categories. J. Pure Appl. Algebra 110 (1996), 219–240. MR 1393114 | Zbl 0858.18004
[4] Coppey L.: Algèbres de decompositions et précatégories. Diagrammes 4 (Suppl.) (1980). MR 0684912 | Zbl 0497.18015
[5] Grandis M., Paré R.: Limits in double categories. Cah. Topol. Géom. Différ. Catég. 40 (1999), 162–220. MR 1716779 | Zbl 0939.18007
[6] Gray J. W.: Formal category theory: adjointness for 2-categories. Lecture Notes in Math. Vol. 391, Springer-Verlag (Berlin 1974). MR 0371990 | Zbl 0285.18006
[7] Korostenski M., Tholen W.: Factorization systems as Eilenberg–Moore algebras. J. Pure Appl. Algebra 85 (1993), 57–72. MR 1207068 | Zbl 0778.18001
[8] Rosický J., Tholen W.: Lax factorization algebras. J. Pure Appl. Algebra 175 (2002), 355–382. MR 1935984 | Zbl 1013.18001
[9] Rosický J., Tholen W.: Factorization, fibration and torsion. preprint (York University 2006). MR 2369170 | Zbl 1184.18009
[10] Rosebrugh R., Wood R. J.: Coherence for factorization algebras. Theory Appl. Categories 10 (2002), 134–147. MR 1883483 | Zbl 0994.18001
Search
Partner of
