| Title:
|
Hereditarity of closure operators and injectivity (English) |
| Author:
|
Castellini, Gabriele |
| Author:
|
Giuli, Eraldo |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
1 |
| Year:
|
1992 |
| Pages:
|
149-157 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A notion of hereditarity of a closure operator with respect to a class of monomorphisms is introduced. Let $C$ be a regular closure operator induced by a subcategory $\Cal A$. It is shown that, if every object of $\Cal A$ is a subobject of an $\Cal A$-object which is injective with respect to a given class of monomorphisms, then the closure operator $C$ is hereditary with respect to that class of monomorphisms. (English) |
| Keyword:
|
closure operator |
| Keyword:
|
hereditary closure operator |
| Keyword:
|
injective object |
| Keyword:
|
factorization pair |
| MSC:
|
18A20 |
| MSC:
|
18A32 |
| MSC:
|
18G05 |
| idZBL:
|
Zbl 0758.18002 |
| idMR:
|
MR1173756 |
| . |
| Date available:
|
2009-01-08T17:54:17Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118480 |
| . |
| Reference:
|
[C] Castellini G.: Closure operators, monomorphisms and epimorphisms in categories of groups.Cahiers Topologie Geom. Differentielle Categoriques 27 (2) (1986), 151-167. Zbl 0592.18001, MR 0850530 |
| Reference:
|
[CS] Castellini G., Strecker G.E.: Global closure operators vs. subcategories.Quaestiones Mathematicae 13 (1990), 417-424. Zbl 0733.18001, MR 1084751 |
| Reference:
|
[DG$_1$] Dikranjan D., Giuli E.: Closure operators induced by topological epireflections.Coll. Math. Soc. J. Bolyai 41 (1983), 233-246. MR 0863906 |
| Reference:
|
[DG$_2$] Dikranjan D., Giuli E.: Closure operators I.Topology Appl 27 (1987), 129-143. Zbl 0634.54008, MR 0911687 |
| Reference:
|
[DG$_3$] Dikranjan D., Giuli E.: Factorizations, injectivity and compactness in categories of modules.Comm. Algebra 19 (1) (1991), 45-83. Zbl 0726.16005, MR 1092551 |
| Reference:
|
[DG$_4$] Dikranjan D., Giuli E.: $C$-perfect morphisms and $C$-compactness.preprint. |
| Reference:
|
[DGT] Dikranjan D., Giuli E., Tholen W.: Closure operators II.Proceedings of the Conference in Categorical Topology (Prague, 1988) World Scientific (1989), 297-335. MR 1047909 |
| Reference:
|
[G] Giuli E.: Bases of topological epireflections.Topology Appl. 11 (1980), 265-273. MR 0585271 |
| Reference:
|
[HS] Herrlich H., Strecker G.E.: Category Theory.2nd ed., Helderman Verlag, Berlin, 1979. Zbl 1125.18300, MR 0571016 |
| Reference:
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[HSS] Herrlich H., Salicrup G., Strecker G.E.: Factorizations, denseness, separation, and relatively compact objects.Topology Appl. 27 (1987), 157-169. Zbl 0629.18003, MR 0911689 |
| Reference:
|
[K] Koslowski J.: Closure operators with prescribed properties.Category Theory and its Applications (Louvain-la-Neuve, 1987) Springer L.N.M. 1248 (1988), 208-220. Zbl 0659.18005, MR 0975971 |
| Reference:
|
[L] Lambek J.: Torsion theories, additive semantics and rings of quotients.Springer L.N.M. 177, 1971. Zbl 0213.31601, MR 0284459 |
| Reference:
|
[S] Salbany S.: Reflective subcategories and closure operators.Proceedings of the Conference in Categorical Topology (Mannheim, 1975), Springer L.N.M. 540 (1976), 548-565. Zbl 0335.54003, MR 0451186 |
| Reference:
|
[Sk] Skula L.: On a reflective subcategory of the category of all topological spaces.Trans. Amer. Mat. Soc. 142 (1969), 37-41. Zbl 0185.50401, MR 0248718 |
| . |
