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.
@article{119036, author = {David Holgate}, title = {Linking the closure and orthogonality properties of perfect morphisms in a category}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {39}, year = {1998}, pages = {587-607}, zbl = {0970.18002}, mrnumber = {1666810}, language = {en}, url = {http://dml.mathdoc.fr/item/119036} }
Holgate, David. Linking the closure and orthogonality properties of perfect morphisms in a category. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) pp. 587-607. http://gdmltest.u-ga.fr/item/119036/
Abstract and Concrete Categories, Pure and Applied Mathematics, John Wiley and Sons, Inc., New York, 1990. | MR 1051419
On factorization of maps through $\tau X$, Colloq. Math. 23 (1971), 45-52. (1971) | MR 0305331 | Zbl 0222.54032
General Topology, Part I, ADIWES International Series in Mathematics, Addison-Wesley Publishing Company, Reading, 1966.
On sequentially proper maps and sequential compactification, J. London Math. Soc. (2) 7 (1973), 515-522. (1973) | MR 0331307
Results on perfectness, unpublished manuscript, 1993.
Topology in a Category: Compactness, Port. Math., to appear. | MR 1432147 | Zbl 0877.18002
On a generalization of perfect maps, unpublished manuscript, 1989. | Zbl 0978.54009
Closure operators I, Topology Appl. 27 (1987), 129-143. (1987) | MR 0911687 | Zbl 0634.54008
unpublished manuscript, 1991, .
Categorical structure of closure operators, Kluwer Academic Publishers, 1995. | MR 1368854 | Zbl 0853.18002
General Topology - Revised and completed edition, Heldermann Verlag, Berlin, 1989. | MR 1039321
On compact and $ Top_{0}$-compact sobrification, Rend. Circ. Mat. Palermo Suppl. II 29 (1992), 399-405. (1992) | MR 1197182
On epireflective hulls II, Notes for Meerut University Summer Institute on Topology, 1971.
Perfect maps and epireflective hulls, Canadian J. Math. 27 (1975), 11-24. (1975) | MR 0365499
Some properties of compactifications, Duke Math. J. 25 (1958), 83-106. (1958) | MR 0096196 | Zbl 0081.38604
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
Perfect subcategories and factorizations, Colloquia Mathematica Societatis János Bolyai 8 (1974), 387-403. (1974) | MR 0362193 | Zbl 0335.54011
Factorisations, denseness, separation and relatively compact objects, Topology Appl. 27 (1987), 157-169. (1987) | MR 0911689
The pullback closure, perfect morphisms and completions, PhD. Thesis, University of Cape Town, 1995.
The pullback closure operator and generalisations of perfectness, Applied Categorical Structures 4 (1996), 107-120. (1996) | MR 1393967 | Zbl 0912.18002
Preservation of products by functors close to reflectors, Topology Appl. 27 (1987), 171-189. (1987) | MR 0911690
Compact Hausdorff objects, Topology Appl. 4 (1974), 341-360. (1974) | MR 0367901 | Zbl 0289.54003
Relations between two reflections, Science Reports T.K.D. Sect. A 12 (324) (1974), 80-88. | MR 0341408 | Zbl 0282.18007
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
Epireflection operators vs perfect morphisms and closed classes of epimorphisms, Bull. Austral. Math. Society 7 (1972), 359-366. (1972) | MR 0322003 | Zbl 0242.18004
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
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
On $E$-compact spaces and generalizations of perfect mappings, Pacific J. Math. 46 (1973), 275-282. (1973) | MR 0324658 | Zbl 0263.54004