Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
(locally) orthogonal $\Cal E$-factorization; (local) factorization class; colimit of a chain; cointersection; regular epimorphism; joint coequalizer; (familially) strong epimorphism; decomposition number
(locally) orthogonal $\Cal E$-factorization; (local) factorization class; colimit of a chain; cointersection; regular epimorphism; joint coequalizer; (familially) strong epimorphism; decomposition number
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.
References:
[1] BörgerR.: Kategorielle Beschreibungen von Zusammenhangsbegriffen. Doctoral Dissertation, Fernuniversität Hagen, 1981. Zbl 0478.18003
[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. MR 0785013 | Zbl 0549.18003
[3] BörgerR., Tholen W.: Total categories and solid functors. Can. J. Math. 42 (1990), 213-229. MR 1051726 | Zbl 0742.18001
[4] BörgerR., Tholen W.: Strong, regular, and dense generators. Cahiers Topologie Géom. Différentielle Catégoriques, to appear. Zbl 0758.18001
[5] Ehrbar H., Wyler O.: Images in categories as reflections. Cahiers Topologie Géom. Différentielle Catégoriques 28 (1987), 143-158. MR 0913969 | Zbl 0632.18001
[6] Freyd P., Kelly G.M.: Categories of continuous functors I. J. Pure Appl. Algebra 2 (1972), 169-191. MR 0322004 | Zbl 0257.18005
[7] Gabriel P., Ulmer F.: Lokal präsentierbare Kategorien. Lecture Notes in Mathematics 221, Springer, Berlin, 1971. MR 0327863 | Zbl 0225.18004
[8] Herrlich H., Salicrup G., Vazquez R.: Dispersed factorization structures. Can. J. Math. 31 (1979), 1059-1071. MR 0546958 | Zbl 0435.18003
[9] Herrlich H., Salicrup G., Vazquez R.: Light factorization structures. Quaest. Math. 3 (1979), 181-213. MR 0533531 | Zbl 0407.54006
[10] Isbell J.R.: Epimorphisms and dominions. Proceedings of the Conference on Categorical Algebra, La Jolla 1965, Springer, Berlin (1966), 232-246. MR 0209202 | Zbl 0287.08007
[11] Isbell J.R.: Structure of categories. Bull. Amer. Math. Soc. 72 (1966), 619-655. MR 0206071 | Zbl 0142.25401
[12] Kelly G.M.: Monomorphisms, epimorphisms, and pullbacks. J. Austral. Math. Soc. A9 (1969), 124-142. MR 0240161
[13] Kunen K.: Set theory. Studies in Logic and the Foundation of Mathematics 102, North-Holland, Amsterdam, 1980. MR 0597342 | Zbl 0960.03033
[14] Melton A., Strecker G.E.: On the structure of factorization structures. Lecture Notes in Mathematics 962, Springer, Berlin (1982), 197-208. MR 0682957 | Zbl 0502.18001
[15] MacDonald J., Stone A.: The tower and regular decomposition. Cahiers Topologie Géom. Différentielle Categoriques 23 (1982), 197-213. MR 0667399 | Zbl 0491.18002
[16] MacDonald J., Tholen W.: Decomposition of morphisms into infinetely many factors. Lecture Notes in Mathematics 962, Springer, Berlin (1982), 175-189. MR 0682955
[17] Preuß G.: $\Cal E$-zusammenhängende Räume. Manuscripta Math. 3 (1970), 331-342. MR 0282323
[18] Street R.: The familial approach to total completeness and toposes. Trans. Amer. Math. Soc. 284 (1984), 355-369. MR 0742429
[19] Street R., Walters R.: Yoneda structures on 2-categories. J. Algebra 50 (1978), 350-379. MR 0463261 | Zbl 0401.18004
[20] Tholen W.: Bildzerlegungen und algebraische Kategorien. Doctoral Dissertation, Universität Münster, 1974.
[21] Tholen W.: Factorizations, localizations and the orthogonal subcategory problem. Math. Nachr. 114 (1983), 63-85. MR 0745048 | Zbl 0553.18003
[22] Tholen W.: MacNeille completions of categories with local properties. Comment. Math. Univ. St. Pauli 28 (1979), 179-202. MR 0578672
Search
Partner of
