Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
perfect morphism; (pullback) closure operator; factorisation theory; orthogonal morphisms
perfect morphism; (pullback) closure operator; factorisation theory; orthogonal morphisms
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.
References:
[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
[2] Blaszczyk A., Mioduszewski J.: On factorization of maps through $\tau X$. Colloq. Math. 23 (1971), 45-52. MR 0305331 | Zbl 0222.54032
[3] Bourbaki N.: General Topology, Part I. ADIWES International Series in Mathematics, Addison-Wesley Publishing Company, Reading, 1966.
[4] Brown R.: On sequentially proper maps and sequential compactification. J. London Math. Soc. (2) 7 (1973), 515-522. MR 0331307
[5] Brümmer G.C.L., Giuli E.: Results on perfectness. unpublished manuscript, 1993.
[6] Clementino M.M., Giuli E., Tholen W.: Topology in a Category: Compactness. Port. Math., to appear. MR 1432147 | Zbl 0877.18002
[7] Dikranjan D.: On a generalization of perfect maps. unpublished manuscript, 1989. Zbl 0978.54009
[8] Dikranjan D., Giuli E.: Closure operators I. Topology Appl. 27 (1987), 129-143. MR 0911687 | Zbl 0634.54008
[9] Dikranjan D., Giuli E. $C$-perfect morphisms and $C$-compactness: unpublished manuscript, 1991.
[10] Dikranjan D., Tholen W.: Categorical structure of closure operators. Kluwer Academic Publishers, 1995. MR 1368854 | Zbl 0853.18002
[11] Engelking R.: General Topology - Revised and completed edition. Heldermann Verlag, Berlin, 1989. MR 1039321
[12] Fedeli A.: On compact and $ Top_{0}$-compact sobrification. Rend. Circ. Mat. Palermo Suppl. II 29 (1992), 399-405. MR 1197182
[13] Franklin S.P.: On epireflective hulls II. Notes for Meerut University Summer Institute on Topology, 1971.
[14] Hager A.W.: Perfect maps and epireflective hulls. Canadian J. Math. 27 (1975), 11-24. MR 0365499
[15] Henriksen M., Isbell J.R.: Some properties of compactifications. Duke Math. J. 25 (1958), 83-106. MR 0096196 | Zbl 0081.38604
[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. MR 0362192 | Zbl 0329.18009
[17] Herrlich H.: Perfect subcategories and factorizations. Colloquia Mathematica Societatis János Bolyai 8 (1974), 387-403. MR 0362193 | Zbl 0335.54011
[18] Herrlich H., Salicrup G., Strecker G.E.: Factorisations, denseness, separation and relatively compact objects. Topology Appl. 27 (1987), 157-169. MR 0911689
[19] Holgate D.: The pullback closure, perfect morphisms and completions. PhD. Thesis, University of Cape Town, 1995.
[20] Holgate D.: The pullback closure operator and generalisations of perfectness. Applied Categorical Structures 4 (1996), 107-120. MR 1393967 | Zbl 0912.18002
[21] Hušek M., de Vries J.: Preservation of products by functors close to reflectors. Topology Appl. 27 (1987), 171-189. MR 0911690
[22] Manes E.G.: Compact Hausdorff objects. Topology Appl. 4 (1974), 341-360. MR 0367901 | Zbl 0289.54003
[23] Nakagawa R.: Relations between two reflections. Science Reports T.K.D. Sect. A 12 (324) (1974), 80-88. MR 0341408 | Zbl 0282.18007
[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. MR 0367894 | Zbl 0294.54011
[25] Strecker G.: Epireflection operators vs perfect morphisms and closed classes of epimorphisms. Bull. Austral. Math. Society 7 (1972), 359-366. MR 0322003 | Zbl 0242.18004
[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. MR 0365457 | Zbl 0289.18004
[27] Strecker G.: Perfect sources. Proc. Conf. Categorical Topology (Mannheim 1975), Lecture Notes in Mathematics 540, Springer-Verlag, Berlin, 1976, pp.605-624. MR 0451192 | Zbl 0338.54007
[28] Tsai J.H.: On $E$-compact spaces and generalizations of perfect mappings. Pacific J. Math. 46 (1973), 275-282. MR 0324658 | Zbl 0263.54004
Search
Partner of
