The pullback closure operator and generalisations of perfectness

Applied Categorical Structures

Volumn 4, Issue 1, 1996, Pages 107-120

  Holgate, David ^a  

^a UNIVERSITY OF CAPE TOWN   (South Africa)

Author keywords

Closure operator; Perfect morphism; Pointed endofunctor

Indexed keywords

EID: 0009090838     PISSN: 09272852     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00124119     Document Type: Article

References (19)

1. Adámek, J., Herrlich, H., and Strecker, G. E.: Abstract and Concrete Categories, Wiley, Inc., New York, 1990.
2. Brümmer, G. C. L. and Giuli. E.: Splitting operators, Unpublished manuscript, 1993.
3. Cassidy, C., Hébert, M., and Kelly, G. M.: Reflective subcategories, localisations and factorisation systems, J. Austral. Math. Soc. Ser. A 38 (1985), 287-329.
4. Castellini, G.: Compact objects, surjectivity of epimorphisms and compactifications, Cahiers Topologie Géom. Différentielle Catégoriques 31 (1990), 53-65.
5. Castellini, G.: Regular closure operators and compactness, Cahiers Topologie Géom. Différentielle Catégoriques 33 (1992), 21-31.
6. Clementino, M., Giuli, E., and Tholen, W.: Compact objects and perfect morphisms, Preprint, 1995.
7. Dikranjan, D.: Semiregular closure operators and epimorphisms in topological categories, Suppl. Rend. Circolo Mat. Palermo (Serie II) 29 (1992), 105-160.
8. Dikranjan, D. and Giuli, E.: Closure Operators I, Topology Appl. 27 (1987), 129-143.
9. Dikranjan, D. and Giuli, E.: C-perfect morphisms and C-compactness, Preprint, 1990.
10. Dikranjan, D., Giuli, E., and Tholen, W.: Closure Operators II, in Categorical Topology and Its Relation to Analysis, Algebra and Combinatorics (Conference Proceedings, Prague 1988) World Scientific, Singapore, 1988, pp. 297-335.
11. Dikranjan, D. and Tholen, W.: Categorical Structure of Closure Operators, Kluwer, Dordrecht, 1995.
12. Fay, T. H. and Walls, G.: Compact nilpotent groups, Communications in Algebra 17(9) (1989), 2255-2268.
13. Herrlich, H.: A generalization of perfect maps, in General Topology and its Relations to Modern Analysis and Algebra III (Prague Symp. 1971) Academia, Prague, 1972, pp. 187-191.
14. Herrlich, H.: Perfect subcategories and factorisations, Colloq. Math. Soc. János Bolyai 8 (1974), 387-403.
15. Herrlich, H., Salicrup, G., and Strecker, G. E.: Factorisations, denseness, separation and relatively compact objects, Topology Appl. 27 (1987), 157-169.
16. Holgate, D.: Closure Operators in Categories, Thesis Reprints 015, University of Cape Town, 1992.
17. Nel, L.: Development classes: An approach to perfectness, reflectiveness and extension problems, in TOPO 72 Proc. Conf. General Topology and Its Applications (Pittsburgh 1972), Lecture Notes in Math. 378, Springer, 1974, pp. 322-340.
18. Strecker, G.: Epireflection operators vs perfect morphisms and closed classes of epimorphisms, Bull. Austral. Math. Soc. 7 (1972), 359-366.
19. Strecker, G.: Perfect sources, in Proc. Conf. Categorical Topology (Mannheim 1975), Lecture Notes in Math. 540, Springer, 1976, pp. 605-624.