| Title:
|
Making factorizations compositive (English) |
| Author:
|
Börger, Reinhard |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
749-759 |
| . |
| Category:
|
math |
| . |
| Summary:
|
The main aim of this paper is to obtain compositive cone factorizations from non-compositive ones by itereration. This is possible if and only if certain colimits of (possibly large) chains exist. In particular, we show that (strong-epi, mono) factorizations of cones exist if and only if joint coequalizers and colimits of chains of regular epimorphisms exist. (English) |
| Keyword:
|
(locally) orthogonal $\Cal E$-factorization |
| Keyword:
|
(local) factorization class |
| Keyword:
|
colimit of a chain |
| Keyword:
|
cointersection |
| Keyword:
|
regular epimorphism |
| Keyword:
|
joint coequalizer |
| Keyword:
|
(familially) strong epimorphism |
| Keyword:
|
decomposition number |
| MSC:
|
03E10 |
| MSC:
|
18A20 |
| MSC:
|
18A30 |
| MSC:
|
18A32 |
| idZBL:
|
Zbl 0760.18001 |
| idMR:
|
MR1159822 |
| . |
| Date available:
|
2009-01-08T17:48:53Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118455 |
| . |
| Reference:
|
[1] BörgerR.: Kategorielle Beschreibungen von Zusammenhangsbegriffen.Doctoral Dissertation, Fernuniversität Hagen, 1981. Zbl 0478.18003 |
| Reference:
|
[2] BörgerR., Tholen W.: Concordant-dissonant and monotone-light.Proceedings of the International Conference on Categorical Topology, Toledo (Ohio), 1983 Sigma Series in Pure Mathematics 5 (1984), 90-107. Zbl 0549.18003, MR 0785013 |
| Reference:
|
[3] BörgerR., Tholen W.: Total categories and solid functors,.Can. J. Math. 42 (1990), 213-229. Zbl 0742.18001, MR 1051726 |
| Reference:
|
[4] BörgerR., Tholen W.: Strong, regular, and dense generators.Cahiers Topologie Géom. Différentielle Catégoriques, to appear. Zbl 0758.18001 |
| Reference:
|
[5] Ehrbar H., Wyler O.: Images in categories as reflections,.Cahiers Topologie Géom. Différentielle Catégoriques 28 (1987), 143-158. Zbl 0632.18001, MR 0913969 |
| Reference:
|
[6] Freyd P., Kelly G.M.: Categories of continuous functors I.J. Pure Appl. Algebra 2 (1972), 169-191. Zbl 0257.18005, MR 0322004 |
| Reference:
|
[7] Gabriel P., Ulmer F.: Lokal präsentierbare Kategorien.Lecture Notes in Mathematics 221, Springer, Berlin, 1971. Zbl 0225.18004, MR 0327863 |
| Reference:
|
[8] Herrlich H., Salicrup G., Vazquez R.: Dispersed factorization structures.Can. J. Math. 31 (1979), 1059-1071. Zbl 0435.18003, MR 0546958 |
| Reference:
|
[9] Herrlich H., Salicrup G., Vazquez R.: Light factorization structures.Quaest. Math. 3 (1979), 181-213. Zbl 0407.54006, MR 0533531 |
| Reference:
|
[10] Isbell J.R.: Epimorphisms and dominions.Proceedings of the Conference on Categorical Algebra, La Jolla 1965, Springer, Berlin (1966), 232-246. Zbl 0287.08007, MR 0209202 |
| Reference:
|
[11] Isbell J.R.: Structure of categories.Bull. Amer. Math. Soc. 72 (1966), 619-655. Zbl 0142.25401, MR 0206071 |
| Reference:
|
[12] Kelly G.M.: Monomorphisms, epimorphisms, and pullbacks.J. Austral. Math. Soc. A9 (1969), 124-142. MR 0240161 |
| Reference:
|
[13] Kunen K.: Set theory.Studies in Logic and the Foundation of Mathematics 102, North-Holland, Amsterdam, 1980. Zbl 0960.03033, MR 0597342 |
| Reference:
|
[14] Melton A., Strecker G.E.: On the structure of factorization structures.Lecture Notes in Mathematics 962, Springer, Berlin (1982), 197-208. Zbl 0502.18001, MR 0682957 |
| Reference:
|
[15] MacDonald J., Stone A.: The tower and regular decomposition.Cahiers Topologie Géom. Différentielle Categoriques 23 (1982), 197-213. Zbl 0491.18002, MR 0667399 |
| Reference:
|
[16] MacDonald J., Tholen W.: Decomposition of morphisms into infinetely many factors.Lecture Notes in Mathematics 962, Springer, Berlin (1982), 175-189. MR 0682955 |
| Reference:
|
[17] Preuß G.: $\Cal E$-zusammenhängende Räume.Manuscripta Math. 3 (1970), 331-342. MR 0282323 |
| Reference:
|
[18] Street R.: The familial approach to total completeness and toposes.Trans. Amer. Math. Soc. 284 (1984), 355-369. MR 0742429 |
| Reference:
|
[19] Street R., Walters R.: Yoneda structures on 2-categories.J. Algebra 50 (1978), 350-379. Zbl 0401.18004, MR 0463261 |
| Reference:
|
[20] Tholen W.: Bildzerlegungen und algebraische Kategorien.Doctoral Dissertation, Universität Münster, 1974. |
| Reference:
|
[21] Tholen W.: Factorizations, localizations and the orthogonal subcategory problem.Math. Nachr. 114 (1983), 63-85. Zbl 0553.18003, MR 0745048 |
| Reference:
|
[22] Tholen W.: MacNeille completions of categories with local properties.Comment. Math. Univ. St. Pauli 28 (1979), 179-202. MR 0578672 |
| . |
