Hostname: page-component-7c8c6479df-7qhmt Total loading time: 0 Render date: 2024-03-28T17:53:47.230Z Has data issue: false hasContentIssue false

Reflective subcategories, localizations and factorizationa systems

Published online by Cambridge University Press:  09 April 2009

C. Cassidy
Affiliation:
Départment de Mathématiques Université LavalQuebec G1 K 7P4, Canada
M. Hébert
Affiliation:
Déepartment de Mathématiques Univesité LavalQuebec G1 K 7P4, Canada
G. M. Kelly
Affiliation:
Pure Mathamatics Department University of SydneyN.S.W. 2006, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This work is a detailed analysis of the relationship between reflective subcategories of a category and factorization systems supported by the category.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Adámek, J., ‘Colimits of algebras revisited’, Bull. Austral. Math. Soc. 17 (1977), 433450.CrossRefGoogle Scholar
[2]Barr, M., ‘Non-abelian torsion theories’, Canad. J. Math. 25 (1973), 12241237.CrossRefGoogle Scholar
[3]Borceux, F., ‘Sheaves of algebras for a commutative theory’, Ann. Soc. Sci. Bruxelles 95 (1981), 319.Google Scholar
[4]Bousfield, A. K., ‘Constructions of factorization systems in categories’, J. Pure Appl. Algebra 9 (1977), 207220.CrossRefGoogle Scholar
[5]Cassidy, C. and Hilton, P. J., ‘L'isolateur d'un homomorphisme de groupes’, Canad. J. Math. 31 (1979), 375390.CrossRefGoogle Scholar
[6]Day, B. J., ‘On adjoint-functor factorization’, Category Seminar Sydney 1972/1973, pp. 119 (Lecture Notes in Math. 420 (1974), Springer-Verlag, Berlin-Heidelberg-New York).Google Scholar
[7]Freyd, P. J. and Kelly, G. M., ‘Categories of continuous functors I’, J. Pure Appl. Algebra 2 (1972), 169191;CrossRefGoogle Scholar
Erratum J. Pure Appl. Algebra. 4 (1974), 121.CrossRefGoogle Scholar
[8]Hilton, P. J., Mislin, G. and Roitberg, J., Localization of nilpotent groups and spaces, (Mathematics Studies 15, North-Holland, Amsterdam, 1975).Google Scholar
[9]Johnstone, P. T., Topos theory, (L. M. S. Monographs 10, Academic Press, London-New York-San Francisco, 1977).Google Scholar
[10]Kelly, G. M., ‘Monomorphisms, epimorphisms, and pull-backs’, J. Austral. Math. Soc. 9 (1969), 124142.CrossRefGoogle Scholar
[11]Kelly, G. M., ‘A unified treatment of transfinite constructions for free algebras, free monoids, colimits, associated sheaves, and so on,’ Bull. Austral. Math. Soc. 22 (1980), 183.CrossRefGoogle Scholar
[12]Kennison, J. F, ‘Full reflective subcategories and generalized covering spaces’, Illinois J. Math. 12 (1968), 353365.CrossRefGoogle Scholar
[13]Popescu, N., Abelian categories with applications to rings and modules, (L. M. S. Monographs 3, Academic Press, London and New York, 1973).Google Scholar
[14]Stenström, B., Rings of quotients (Grundlehren der Math. Wiss. 217, Springer-Verlag, Berlin-Heidelberg-New York, 1975).CrossRefGoogle Scholar