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.
@article{118455, author = {Reinhard B\"orger}, title = {Making factorizations compositive}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {32}, year = {1991}, pages = {749-759}, zbl = {0760.18001}, mrnumber = {1159822}, language = {en}, url = {http://dml.mathdoc.fr/item/118455} }
Börger, Reinhard. Making factorizations compositive. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 749-759. http://gdmltest.u-ga.fr/item/118455/
Kategorielle Beschreibungen von Zusammenhangsbegriffen, Doctoral Dissertation, Fernuniversität Hagen, 1981. | Zbl 0478.18003
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. (1984) | MR 0785013 | Zbl 0549.18003
Total categories and solid functors,, Can. J. Math. 42 (1990), 213-229. (1990) | MR 1051726 | Zbl 0742.18001
Strong, regular, and dense generators, Cahiers Topologie Géom. Différentielle Catégoriques, to appear. | Zbl 0758.18001
Images in categories as reflections,, Cahiers Topologie Géom. Différentielle Catégoriques 28 (1987), 143-158. (1987) | MR 0913969 | Zbl 0632.18001
Categories of continuous functors I, J. Pure Appl. Algebra 2 (1972), 169-191. (1972) | MR 0322004 | Zbl 0257.18005
Lokal präsentierbare Kategorien, Lecture Notes in Mathematics 221, Springer, Berlin, 1971. | MR 0327863 | Zbl 0225.18004
Dispersed factorization structures, Can. J. Math. 31 (1979), 1059-1071. (1979) | MR 0546958 | Zbl 0435.18003
Light factorization structures, Quaest. Math. 3 (1979), 181-213. (1979) | MR 0533531 | Zbl 0407.54006
Epimorphisms and dominions, Proceedings of the Conference on Categorical Algebra, La Jolla 1965, Springer, Berlin (1966), 232-246. | MR 0209202 | Zbl 0287.08007
Structure of categories, Bull. Amer. Math. Soc. 72 (1966), 619-655. (1966) | MR 0206071 | Zbl 0142.25401
Monomorphisms, epimorphisms, and pullbacks, J. Austral. Math. Soc. A9 (1969), 124-142. (1969) | MR 0240161
Set theory, Studies in Logic and the Foundation of Mathematics 102, North-Holland, Amsterdam, 1980. | MR 0597342 | Zbl 0960.03033
On the structure of factorization structures, Lecture Notes in Mathematics 962, Springer, Berlin (1982), 197-208. | MR 0682957 | Zbl 0502.18001
The tower and regular decomposition, Cahiers Topologie Géom. Différentielle Categoriques 23 (1982), 197-213. (1982) | MR 0667399 | Zbl 0491.18002
Decomposition of morphisms into infinetely many factors, Lecture Notes in Mathematics 962, Springer, Berlin (1982), 175-189. | MR 0682955
$\Cal E$-zusammenhängende Räume, Manuscripta Math. 3 (1970), 331-342. (1970) | MR 0282323
The familial approach to total completeness and toposes, Trans. Amer. Math. Soc. 284 (1984), 355-369. (1984) | MR 0742429
Yoneda structures on 2-categories, J. Algebra 50 (1978), 350-379. (1978) | MR 0463261 | Zbl 0401.18004
Bildzerlegungen und algebraische Kategorien, Doctoral Dissertation, Universität Münster, 1974.
Factorizations, localizations and the orthogonal subcategory problem, Math. Nachr. 114 (1983), 63-85. (1983) | MR 0745048 | Zbl 0553.18003
MacNeille completions of categories with local properties, Comment. Math. Univ. St. Pauli 28 (1979), 179-202. (1979) | MR 0578672