| Title:
|
Totality of colimit closures (English) |
| Author:
|
Börger, Reinhard |
| Author:
|
Tholen, Walter |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
761-768 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Adámek, Herrlich, and Reiterman showed that a cocomplete category $\Cal A$ is cocomplete if there exists a small (full) subcategory $\Cal B$ such that every $\Cal A$-object is a colimit of $\Cal B$-objects. The authors of the present paper strengthened the result to totality in the sense of Street and Walters. Here we weaken the hypothesis, assuming only that the colimit closure is attained by transfinite iteration of the colimit closure process up to a fixed ordinal. This requires some investigations on generalized notions of generators. (English) |
| Keyword:
|
cocomplete category |
| Keyword:
|
(almost-)$\Cal E$-generator |
| Keyword:
|
colimit closure |
| Keyword:
|
cointersection |
| Keyword:
|
total category |
| MSC:
|
18A20 |
| MSC:
|
18A30 |
| MSC:
|
18A35 |
| MSC:
|
18A40 |
| MSC:
|
18B99 |
| idZBL:
|
Zbl 0760.18002 |
| idMR:
|
MR1159823 |
| . |
| Date available:
|
2009-01-08T17:48:58Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118456 |
| . |
| Reference:
|
[1] Adámek J., Herrlich H., Reiterman J.: Cocompleteness almost implies completeness. Proc. Conf. Cat. Top. Prague, World Scientific, Singapore, 1989.. MR 1047905 |
| Reference:
|
[2] Börger R.: Making factorizations compositive.Comment. Math. Univ. Carolinae 32 (1991), 749-759. MR 1159822 |
| Reference:
|
[3] Börger R., 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 |
| Reference:
|
[4] Börger R., Tholen W.: Total categories and solid functors.Canad. J. Math. 42 (1990), 213-229. MR 1051726 |
| Reference:
|
[5] Börger R., Tholen W.: Strong, regular, and dense generators.Cahiers Topologie Géom. Différentielle Catégoriques, to appear. MR 1158111 |
| Reference:
|
[6] Day B.: Further criteria for totality.Cahiers Topologie Géom. Différentielle Catégoriques 28 (1987), 77-78. Zbl 0626.18001, MR 0903153 |
| Reference:
|
[7] Isbell J.R.: Structure of categories.Bull. Amer. Math. Soc. 72 (1966), 619-655. Zbl 0142.25401, MR 0206071 |
| Reference:
|
[8] Kelly G.M.: Monomorphisms, epimorphisms, and pullbacks.J. Austral. Math. Soc. A9 (1969), 124-142. MR 0240161 |
| Reference:
|
[9] Kelly G.M.: A survey on totality for enriched and ordinary categories.Cahiers Topologie Géom. Différentielle Catégoriques 27 (1986), 109-131. MR 0850527 |
| Reference:
|
[10] Kunen K.: Set theory.Studies in Logic and the Foundation of Mathematics 102, North-Holland, Amsterdam, 1980. Zbl 0960.03033, MR 0597342 |
| Reference:
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[11] MacDonald J., Stone A.: Essentially monadic adjunctions.Lecture Notes in Mathematics 962, Springer, Berlin (1982), 167-174. Zbl 0498.18003, MR 0682954 |
| Reference:
|
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| Reference:
|
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| . |
