Functorial factorization, well-pointedness and separability

Journal of Pure and Applied Algebra

Volumn 142, Issue 2, 1999, Pages 99-130

  Janelidze, George ^a   Tholen, Walter ^a  

^a YORK UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033569279     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-4049(98)00095-4     Document Type: Article

References (45)

1. J. Adámek, W. Tholen, Total categories with generators, J. Algebra 133 (1990) 63-78.
2. M. Barr, On categories with effective unions, Lecture Notes in Math., vol. 1348, Springer, Berlin, 1988, pp. 19-35.
3. F. Borceux, G.M. Kelly, On locales of localizations, J. Pure Appl. Algebra 46 (1987) 1-34.
4. R. Börger, W. Tholen, Concordant-dissonant and monotone-light, in: Proc. Conf. on Categorical Topology, Toledo, OH 1983, Heldermann Verlag, Berlin, 1984, pp. 90-107.
5. G.C.L. Brümmer, E. Giuli, Splitting Operators, preprint, 1997.
6. A. Carboni, G. Janelidze, Decidable (= separable) objects and morphisms in lextensive categories, J. Pure Appl. Algebra 110 (1996) 219-240.
7. A. Carboni, S. Mantovani, An elementary characterization of categories of separated objects, J. Pure Appl. Algebra 89 (1993) 63-92.
8. A. Carboni, G. Janelidze, R.A. Magid, A note on the Galois correspondence for fommutative rings, J. Algebra 183 (1996) 266-272.
9. A. Carboni, G. Janelidze, G.M. Kelly, P. Paré, On localization and stabilization for factorization systems, Appl. Categor. Struct. 5 (1997) 1-58.
10. C. Cassidy, M. Hébert, G.M. Kelly, Reflective subcategories, localizations, and factorization systems, J. Austral Math. Soc. (Ser. A) 38 (1985) 387-429.
11. M.M. Clementino, Weakly hereditary closure operators, Topology Appl. 49 (1993) 129-139.
12. M.M. Clementino, W. Tholen, Separated and connected maps, Appl. Categor. Struct., to appear.
13. P.J. Collins, Concordant mappings and the concordant-dissonant factorization of an arbitrary continuous function, Proc. Amer. Math. Soc. 27 (1971) 587-591.
14. P.J. Collins, R. Dyckhoff, Connexion properties and factorisation theorems, Quaestiones Math. 2 (1977) 103-112.
15. L. Coppey, Algèbres de décompositions et précatégories, Diagrammes 3 (Suppl.) 1980.
16. D. Dikranjan, W. Tholen, Categorical Structure of Closure Operators, Kluwer Academic Publishers, Dordrecht, 1995.
17. D. Dikranjan, E. Giuli, W. Tholen, Closure operators II, in: Proc. Int. Conf. on Categorical Topology, Prague, 1988, World Scientific, Singapore, 1989, pp. 297-335.
18. R. Dyckhoff, Factorisation theorems and projective spaces in topology, Math. Z. 127 (1972) 256-264.
19. H. Ehrbar, O. Wyler, Images in categories as reflections, Cahiers Topologie Géom. Différentielle Catégoriques 28 (1987) 143-159.
20. P.J. Freyd, G.M. Kelly, Categories of continuous functors, I, J. Pure Appl. Algebra 2 (1972) 169-191.
21. H. Herrlich, Perfect subcategories and factorizations, in: Colloq. Math. Soc. Janos Bolyai, 8. Topics in Topology, Keszthely Hungary 1972, North-Holland, Amsterdam, 1974, pp. 387-493.
22. H. Herrlich, G. Salicrup, R. Vázquez, Dispersed factorization structures, Canad. J. Math. 31 (1979) 1059-1071.
23. D. Holgate, The pullback closure and general generalisations of perfectness, Appl. Categor. Struct. 4 (1996) 107-120.
24. G.B. Im, G.M. Kelly, On classes of morphisms closed under limits, J. Korean Math. Soc. 23 (1986) 1-18.
25. J.R. Isbell, Some remarks concerning categories and subspaces, Canad. J. Math. 9 (1957) 563-577.
26. G. Janelidze (G.Z. Dzhanelidze), The fundamental theorem of Galois theory, Math. USSR-Sb. 64 (1989) 359-374.
27. G. Janelidze, G.M. Kelly, Galois theory and a general notion of central extension, J. Pure Appl. Algebra 97 (1994) 135-161.
28. G. Janelidze, G.M. Kelly, The reflectiveness of covering morphisms in algebra and geometry, Theory Appl. Categories 3 (1997) 132-159.
29. G. Janelidze, W. Tholen, Galois theory of locally dissonant morphisms, J. Pure Appl. Algebra 143 (1999).
30. G.M. Kelly, A unified treatment of transfinite constructions for free algebras, free monoids, colimits, associated sheaves, and so on, Bull. Austral. Math. Soc. 22 (1980) 1-83.
31. M. Korostenski, W. Tholen, On left-cancellable classes of morphisms, Comm. Algebra 14 (1986) 741-766.
32. M. Korostenski, W. Tholen, Factorization systems as Eilenberg-Moore algebras, J. Pure Appl. Algebra 85 (1993) 57-72.
33. J.F. Kennison, Full reflective subcategories and generalized covering spaces, Ill, J. Math. 12 (1968) 353-365.
34. F.E.J. Linton, Coequalizers in categories of algebras, Lecture Notes in Math., vol. 80, Springer, Berlin, 1969, pp. 75-90.
35. J. MacDonald, W. Tholen, Decomposition of morphisms into infinitely many factors, Lecture Notes in Math., vol. 962, Springer, Berlin, 1982, pp. 175-182.
36. S. Mac Lane, Duality for groups, Bull. Amer. Math. Soc. 56 (1950) 485-516.
37. S. Mac Lane, R. Paré, Coherence for bicategories and indexed categories, J. Pure Appl. Algebra 37 (1985) 59-80.
38. R. Paré, D. Schumacher, Abstract families and the adjoint functor theorem, Lecture Notes in Math., vol. 661, Springer, Berlin, 1978, pp. 1-125.
39. D. Pumplün, Universelle und spezielle probleme, Math. Ann. 198 (1972) 131-146.
40. C.M. Ringel, Diagonalisierungspaare I, Math. Z. 112 (1970) 248-266.
41. G.E. Strecker, Component properties and factorizations, Math. Center Tracts 52 (1974) 123-140.
42. W. Tholen, Relative Bildzerlegungen und Algebraische Kategorien, Doctoral Dissertation, Münster, 1974.
43. W. Tholen, Semi-topological functors I, J. Pure Appl. Algebra 15 (1979) 53-73.
44. W. Tholen, Factorizations, localizations and the orthogonal subcategory problem, Math. Nachr. 114 (1983) 63-85.
45. W. Tholen, Prereflections and reflections, Comm. Algebra 14 (1987) 717-740.