Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
closure operator; hereditary closure operator; injective object; factorization pair
closure operator; hereditary closure operator; injective object; factorization pair
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.
References:
[C] Castellini G.: Closure operators, monomorphisms and epimorphisms in categories of groups. Cahiers Topologie Geom. Differentielle Categoriques 27 (2) (1986), 151-167. MR 0850530 | Zbl 0592.18001
[CS] Castellini G., Strecker G.E.: Global closure operators vs. subcategories. Quaestiones Mathematicae 13 (1990), 417-424. MR 1084751 | Zbl 0733.18001
[DG$_1$] Dikranjan D., Giuli E.: Closure operators induced by topological epireflections. Coll. Math. Soc. J. Bolyai 41 (1983), 233-246. MR 0863906
[DG$_2$] Dikranjan D., Giuli E.: Closure operators I. Topology Appl 27 (1987), 129-143. MR 0911687 | Zbl 0634.54008
[DG$_3$] Dikranjan D., Giuli E.: Factorizations, injectivity and compactness in categories of modules. Comm. Algebra 19 (1) (1991), 45-83. MR 1092551 | Zbl 0726.16005
[DG$_4$] Dikranjan D., Giuli E.: $C$-perfect morphisms and $C$-compactness. preprint.
[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
[G] Giuli E.: Bases of topological epireflections. Topology Appl. 11 (1980), 265-273. MR 0585271
[HS] Herrlich H., Strecker G.E.: Category Theory. 2nd ed., Helderman Verlag, Berlin, 1979. MR 0571016 | Zbl 1125.18300
[HSS] Herrlich H., Salicrup G., Strecker G.E.: Factorizations, denseness, separation, and relatively compact objects. Topology Appl. 27 (1987), 157-169. MR 0911689 | Zbl 0629.18003
[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. MR 0975971 | Zbl 0659.18005
[L] Lambek J.: Torsion theories, additive semantics and rings of quotients. Springer L.N.M. 177, 1971. MR 0284459 | Zbl 0213.31601
[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. MR 0451186 | Zbl 0335.54003
[Sk] Skula L.: On a reflective subcategory of the category of all topological spaces. Trans. Amer. Mat. Soc. 142 (1969), 37-41. MR 0248718 | Zbl 0185.50401
Search
Partner of
