| Title:
|
Linking the closure and orthogonality properties of perfect morphisms in a category (English) |
| Author:
|
Holgate, David |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
3 |
| Year:
|
1998 |
| Pages:
|
587-607 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We define perfect morphisms to be those which are the pullback of their image under a given endofunctor. The interplay of these morphisms with other generalisations of perfect maps is investigated. In particular, closure operator theory is used to link closure and ortho\-go\-na\-lity properties of such morphisms. A number of detailed examples are given. (English) |
| Keyword:
|
perfect morphism |
| Keyword:
|
(pullback) closure operator |
| Keyword:
|
factorisation theory |
| Keyword:
|
orthogonal morphisms |
| MSC:
|
18A20 |
| MSC:
|
18B30 |
| MSC:
|
54B30 |
| MSC:
|
54C10 |
| idZBL:
|
Zbl 0970.18002 |
| idMR:
|
MR1666810 |
| . |
| Date available:
|
2009-01-08T18:46:40Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119036 |
| . |
| Reference:
|
[1] Adámek J., Herrlich H., Strecker G.E.: Abstract and Concrete Categories.Pure and Applied Mathematics, John Wiley and Sons, Inc., New York, 1990. MR 1051419 |
| Reference:
|
[2] Blaszczyk A., Mioduszewski J.: On factorization of maps through $\tau X$.Colloq. Math. 23 (1971), 45-52. Zbl 0222.54032, MR 0305331 |
| Reference:
|
[3] Bourbaki N.: General Topology, Part I.ADIWES International Series in Mathematics, Addison-Wesley Publishing Company, Reading, 1966. |
| Reference:
|
[4] Brown R.: On sequentially proper maps and sequential compactification.J. London Math. Soc. (2) 7 (1973), 515-522. MR 0331307 |
| Reference:
|
[5] Brümmer G.C.L., Giuli E.: Results on perfectness.unpublished manuscript, 1993. |
| Reference:
|
[6] Clementino M.M., Giuli E., Tholen W.: Topology in a Category: Compactness.Port. Math., to appear. Zbl 0877.18002, MR 1432147 |
| Reference:
|
[7] Dikranjan D.: On a generalization of perfect maps.unpublished manuscript, 1989. Zbl 0978.54009 |
| Reference:
|
[8] Dikranjan D., Giuli E.: Closure operators I.Topology Appl. 27 (1987), 129-143. Zbl 0634.54008, MR 0911687 |
| Reference:
|
[9] Dikranjan D., Giuli E. $C$-perfect morphisms and $C$-compactness: unpublished manuscript, 1991.. |
| Reference:
|
[10] Dikranjan D., Tholen W.: Categorical structure of closure operators.Kluwer Academic Publishers, 1995. Zbl 0853.18002, MR 1368854 |
| Reference:
|
[11] Engelking R.: General Topology - Revised and completed edition.Heldermann Verlag, Berlin, 1989. MR 1039321 |
| Reference:
|
[12] Fedeli A.: On compact and $ Top_{0}$-compact sobrification.Rend. Circ. Mat. Palermo Suppl. II 29 (1992), 399-405. MR 1197182 |
| Reference:
|
[13] Franklin S.P.: On epireflective hulls II.Notes for Meerut University Summer Institute on Topology, 1971. |
| Reference:
|
[14] Hager A.W.: Perfect maps and epireflective hulls.Canadian J. Math. 27 (1975), 11-24. MR 0365499 |
| Reference:
|
[15] Henriksen M., Isbell J.R.: Some properties of compactifications.Duke Math. J. 25 (1958), 83-106. Zbl 0081.38604, MR 0096196 |
| Reference:
|
[16] Herrlich H.: A generalization of perfect maps.General Topology and its Relation to Modern Analysis and Algebra (Conference Proceedings, Prague, 1971); Academia, Prague, 1972, pp.187-191. Zbl 0329.18009, MR 0362192 |
| Reference:
|
[17] Herrlich H.: Perfect subcategories and factorizations.Colloquia Mathematica Societatis János Bolyai 8 (1974), 387-403. Zbl 0335.54011, MR 0362193 |
| Reference:
|
[18] Herrlich H., Salicrup G., Strecker G.E.: Factorisations, denseness, separation and relatively compact objects.Topology Appl. 27 (1987), 157-169. MR 0911689 |
| Reference:
|
[19] Holgate D.: The pullback closure, perfect morphisms and completions.PhD. Thesis, University of Cape Town, 1995. |
| Reference:
|
[20] Holgate D.: The pullback closure operator and generalisations of perfectness.Applied Categorical Structures 4 (1996), 107-120. Zbl 0912.18002, MR 1393967 |
| Reference:
|
[21] Hušek M., de Vries J.: Preservation of products by functors close to reflectors.Topology Appl. 27 (1987), 171-189. MR 0911690 |
| Reference:
|
[22] Manes E.G.: Compact Hausdorff objects.Topology Appl. 4 (1974), 341-360. Zbl 0289.54003, MR 0367901 |
| Reference:
|
[23] Nakagawa R.: Relations between two reflections.Science Reports T.K.D. Sect. A 12 (324) (1974), 80-88. Zbl 0282.18007, MR 0341408 |
| Reference:
|
[24] Nel L.D.: Development classes: An approach to perfectness, reflectiveness and extension problems.TOPO-72 General Topology and its Applications (Conference Proceedings, Pittsburgh, 1972). Lecture Notes in Mathematics 378, Springer Verlag, Berlin, 1974, pp.322-340. Zbl 0294.54011, MR 0367894 |
| Reference:
|
[25] Strecker G.: Epireflection operators vs perfect morphisms and closed classes of epimorphisms.Bull. Austral. Math. Society 7 (1972), 359-366. Zbl 0242.18004, MR 0322003 |
| Reference:
|
[26] Strecker G.: On characterizations of perfect morphisms and epireflective hulls.TOPO-72 General Topology and its Applications (Conference Proceedings, Pittsburgh, 1972). Lecture Notes in Mathematics 378, Springer Verlag, Berlin, 1974, pp.468-500. Zbl 0289.18004, MR 0365457 |
| Reference:
|
[27] Strecker G.: Perfect sources.Proc. Conf. Categorical Topology (Mannheim 1975), Lecture Notes in Mathematics 540, Springer-Verlag, Berlin, 1976, pp.605-624. Zbl 0338.54007, MR 0451192 |
| Reference:
|
[28] Tsai J.H.: On $E$-compact spaces and generalizations of perfect mappings.Pacific J. Math. 46 (1973), 275-282. Zbl 0263.54004, MR 0324658 |
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