Coreflective subcategories
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- by Horst Herrlich and George E. Strecker PDF
- Trans. Amer. Math. Soc. 157 (1971), 205-226 Request permission
Abstract:
General morphism factorization criteria are used to investigate categorical reflections and coreflections, and in particular epi-reflections and monocoreflections. It is shown that for most categories with “reasonable” smallness and completeness conditions, each coreflection can be “split” into the composition of two mono-coreflections and that under these conditions mono-coreflective subcategories can be characterized as those which are closed under the formation of coproducts and extremal quotient objects. The relationship of reflectivity to closure under limits is investigated as well as coreflections in categories which have “enough” constant morphisms.References
-
S. Baron, Reflective subcategories of colocally small categories, Notices Amer. Math. Soc. 13 (1966), 609. Abstract #636-112.
—, Reflective subcategories of colocally small (cowell powered) categories. II, Notices Amer. Math. Soc. 14 (1967), 516-517. Abstract #67T-331.
- N. Bourbaki, Éléments de mathématique. VII. Première partie: Les structures fondamentales de l’analyse. Livre II: Algèbre. Chapitre III: Algèbre multilinéaire, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1044, Hermann & Cie, Paris, 1948 (French). MR 0026989
- Eduard Čech, On bicompact spaces, Ann. of Math. (2) 38 (1937), no. 4, 823–844. MR 1503374, DOI 10.2307/1968839
- Peter Freyd, Abelian categories. An introduction to the theory of functors, Harper’s Series in Modern Mathematics, Harper & Row, Publishers, New York, 1964. MR 0166240
- Andrew M. Gleason, Universal locally connected refinements, Illinois J. Math. 7 (1963), 521–531. MR 164315
- Horst Herrlich, On the concept of reflections in general topology, Contributions to Extension Theory of Topological Structures (Proc. Sympos., Berlin, 1967) Deutscher Verlag Wissensch., Berlin, 1969, pp. 105–114. MR 0284986 —, Constant maps in categories (to appear).
- H. Herrlich and J. van der Slot, Properties which are closely related to compactness, Nederl. Akad. Wetensch. Proc. Ser. A 70=Indag. Math. 29 (1967), 524–529. MR 0222848 P. J. Hilton, Catégories non-Abéliennes, Lecture Notes, University of Montreal, 1964.
- Miroslav Hušek, Remarks on reflections, Comment. Math. Univ. Carolinae 7 (1966), 249–259. MR 202800
- Miroslav Hušek, One more remark on reflections, Comment. Math. Univ. Carolinae 8 (1967), 129–137. MR 209334
- J. R. Isbell, Some remarks concerning categories and subspaces, Canadian J. Math. 9 (1957), 563–577. MR 94405, DOI 10.4153/CJM-1957-064-6
- J. R. Isbell, Natural sums and abelianizing, Pacific J. Math. 14 (1964), 1265–1281. MR 179230 —, Subobjects, adequacy, completeness and categories of algebras, Rozprawy Mat. 36 (1964). MR 29 #1238.
- John R. Isbell, Structure of categories, Bull. Amer. Math. Soc. 72 (1966), 619–655. MR 206071, DOI 10.1090/S0002-9904-1966-11541-0
- J. F. Kennison, Reflective functors in general topology and elsewhere, Trans. Amer. Math. Soc. 118 (1965), 303–315. MR 174611, DOI 10.1090/S0002-9947-1965-0174611-9
- J. F. Kennison, Full reflective subcategories and generalized covering spaces, Illinois J. Math. 12 (1968), 353–365. MR 227247
- Barry Mitchell, Theory of categories, Pure and Applied Mathematics, Vol. XVII, Academic Press, New York-London, 1965. MR 0202787
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 157 (1971), 205-226
- MSC: Primary 18.10
- DOI: https://doi.org/10.1090/S0002-9947-1971-0280561-2
- MathSciNet review: 0280561