On Localization and Stabilization for Factorization Systems

Applied Categorical Structures

Volumn 5, Issue 1, 1997, Pages 1-58

  Carboni, A ^a   Janelidze, G ^b   Kelly, G M ^c   Pare R ^d  

^a UNIVERSITY OF GENOA   (Italy)

^b INSTITUTE OF PHYSICS   (Georgia)

^c UNIVERSITY OF SYDNEY   (Australia)

^d DALHOUSIE UNIVERSITY   (Canada)

Author keywords

Category; Descent theory; Factorization system; Galois theory; Hereditary torsion theory; Localization; Monotone light factorization; Separable and purely inseparable field extensions; Stabilization

Indexed keywords

EID: 0002404148     PISSN: 09272852     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008620404444     Document Type: Article

References (25)

1. Barr, M. and Diaconescu, R.: On locally simply connected toposes and their fundamental groups, Cahiers Topologie Géom. Différentielle 22 (1981), 301-314.
2. Bourbaki, N.: General Topology, Hermann, Paris, 1966.
3. Bousfield, A. K.: Constructions of factorization systems in categories, J. Pure Appl. Algebra 9 (1977), 207-220.
4. Carboni, A.: Some free constructions in realizability and proof theory, J. Pure Appl. Algebra 103 (1995), 117-148.
5. Carboni, A., Lack, S., and Walters, R. F. C.: Introduction to extensive and distributive categories, J. Pure Appl. Algebra 84 (1993), 145-158.
6. Cassidy, C., Hébert, M., and Kelly, G. M.: Reflective subcategories, localizations and factorization systems, J. Austral. Math. Soc. (Ser. A) 38 (1985), 287-329.
7. Eilenberg, S.: Sur les transformations continues d'espaces métriques compacts, Fund. Math. 22 (1934), 292-296.
8. Freyd, P. J. and Kelly, G. M.: Categories of continuous functors I, J. Pure Appl. Algebra 2 (1972), 169-191.
9. Im, G. B. and Kelly, G. M.: On classes of morphisms closed under limits, J. Korean Math. Soc. 23 (1986), 1-18.
10. Isbell, J.: Subobjects, adequacy, completeness and categories of algebras, Rozprawy Mat. 36 (1964), 1-32.
11. Jacobson, N.: Lectures in Abstract Algebra III. Theory of Fields and Galois Theory, Springer, New York, Heidelberg, Berlin, 1964.
12. Janelidze, G. (Dzhanelidze, G. Z.): The fundamental theorem of Galois theory, Math. USSR-Sb. 64 (1989), 359-374.
13. Janelidze, G.: Pure Galois theory in categories, J. Algebra 132 (1990), 270-286.
14. Janelidze, G.: Precategories and Galois theory, in Category Theory Proceedings Como 1990, Lecture Notes in Mathematics 1488, Springer, Berlin, 1991, pp. 157-173.
15. Janelidze, G. and Kelly, G. M.: Galois theory and a general notion of central extension, J. Pure Appl. Algebra 97 (1994), 135-161.
16. Janelidze, G., Márki, L., and Tholen, W.: Extension classes, coverings and descent data, Preprint, York Univ., 1994.
17. Janelidze, G. and Tholen, W.: Facets of descent, I, Appl. Categorical Structures 2 (1994), 245-281.
18. Janelidze, G. and Tholen, W.: Facets of descent, II, Preprint, York Univ., 1994.
19. MacDonald, J. and Tholen, W.: Decomposition of morphisms into infinitely many factors, in Category Theory Proceedings Gummersbach 1981, Lecture Notes in Mathematics 962, Springer, Berlin, 1982, pp. 175-189.
20. Mac Lane, S.: Categories for the Working Mathematician, Springer, New York, Heidelberg, Berlin, 1971.
21. Reiterman, J., Sobral, M., and Tholen, W.: Composites of effective descent maps, Cahiers Topologie Géom. Différentielle Catégoriques 34 (1993), 193-207.
22. Sobral, M. and Tholen, W.: Effective descent morphisms and effective equivalence relations, in Canadian Mathematical Society Conference Proceedings, Amer. Math. Soc., Providence, 1992, pp. 421-431.
23. Tholen, W.: Factorizations, localizations, and the orthogonal subcategory problem, Math. Nachr. 114 (1983), 63-85.
24. van der Waerden, B. L.: Algebra (Erster Teil), 7te Auflage, Springer, Berlin, 1966.
25. Whyburn, G. T.: Open mappings on locally compact spaces, Memoirs Amer. Math. Soc. 1 (1950).