On semi weak factorization structures

Document Type: Research Paper

Authors

1 Department of Pure Mathematics, Faculty of Math and Computer, Shahid Bahonar University of Kerman

2 Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

3 Department of Pure Mathematics, Faculty of Math and Computers, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

In this article the notions of semi weak orthogonality and semi weak factorization structure in a category $\mathcal X$ are introduced. Then the relationship between semi weak factorization structures and quasi right (left) and weak factorization structures is given. The main result is a characterization of semi weak orthogonality, factorization of morphisms, and semi weak factorization structures by natural isomorphisms.

Keywords


[1] Adamek, J., Herrlich, H., Rosicky, J., and Tholen, W., Weak Factorization Systems and Topological functors, Appl. Categ. Structures 10 (2002), 237-249.
[2] Adamek, J., Herrlich, H., and Strecker, G.E., “Abstract and Concrete Categories”, John Wiely and Sons Inc., 1990. (Also available at: http://www.tac.mta.ca/tac/reprints/articles/17/tr17.pdf.)
[3] Borceux, F., “Handbook of Categorical Algebra; vol. 1, Basic Category Theory”, Cambridge University Press, 1994.
[4] Dikranjan, D. and Tholen, W., “Categorical Structure of Closure Operators”, Kluwer Academic Publishers, 1995.
[5] Hirschhorn, P., “Model Categories and Their Localizations”, Amer. Math. Soc., Math. Survey and Monographs 99, 2002.
[6] Hosseini, S.N. and Mousavi, S.Sh., A relation between closure operators on a small category and its category of  resheaves, Appl. Categ. Structures 14 (2006), 99-110.
[7] Hosseini, S.N. and Mousavi, S.Sh., Quasi left factorization structures as presheaves, Appl. Categ. Structures 22 (2014), 501-514.
[8] Maclane, S. and Moerdijk, I., “Sheaves in Geometry and Logic, A First Introduction to Topos Theory”, Springer-Verlag, 1992.
[9] Mousavi, S.Sh. and Hosseini, S.N., Quasi right factorization structures as presheaves, Appl. Categ. Structures 19 (2011), 741-756.
[10] Piccinini, R.A.,“Lectures on Homotopy Theory”, North-Holland Mathematics Studies 171, 1992.
[11] Rosicky, J. and Tholen, W., Factorization, fibration and torsion, J. Homotopy Relat. Struct. 2(2) (2007), 295-314.
[12] Wisbauer, R., “Foundations of Module and Ring Theory: A Handbook for Study and Research”, Revised and translated from the 1988 German edition, Algebra, Logic and Applications 3., Gordon and Breach Science Publishers, 1991.