Co-well-powered reflective subcategories

Hoffmann, Rudolf-E.

doi:10.1090/S0002-9939-1984-0722413-1

Co-well-powered reflective subcategories

Author: Rudolf-E. Hoffmann
Journal: Proc. Amer. Math. Soc. 90 (1984), 45-46
MSC: Primary 18A40
DOI: https://doi.org/10.1090/S0002-9939-1984-0722413-1
MathSciNet review: 722413
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A full isomorphism-closed subcategory $\mathcal{A}$ of a complete well-powered and co-well-powered category $\mathcal{C}$ is both co-well-powered (in its own right) and reflective in $\mathcal{C}$ if and only if

(a) $\mathcal{A}$ is closed in $\mathcal{C}$ under the formation of (-small-indexed) limits, and

(b) the epi-reflective hull $\mathcal{B}$ of $\mathcal{A}$ in $\mathcal{C}$ is co-well-powered.

[1] S. Baron, Reflectors as compositions of epi-reflectors, Trans. Amer. Math. Soc. 136 (1969), 499–508. MR 0236237, https://doi.org/10.1090/S0002-9947-1969-0236237-1
[2] 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
[3] Horst Herrlich, Topologische Reflexionen und Coreflexionen, Lecture Notes in Mathematics, No. 78, Springer-Verlag, Berlin-New York, 1968 (German). MR 0256332
[4] H. Herrlich, Epireflective subcategories of TOP need not be cowellpowered, Comment. Math. Univ. Carolinae 16 (1975), no. 4, 713–716. MR 0425882
[5] Rudolf-E. Hoffmann, Factorization of cones. II. With applications to weak Hausdorff spaces, Categorical aspects of topology and analysis (Ottawa, Ont., 1980) Lecture Notes in Math., vol. 915, Springer, Berlin-New York, 1982, pp. 148–170. MR 659890
[6] J. R. Isbell, Natural sums and abelianizing, Pacific J. Math. 14 (1964), 1265–1281. MR 0179230
[7] J. F. Kennison, Full reflective subcategories and generalized covering spaces, Illinois J. Math. 12 (1968), 353–365. MR 0227247