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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Co-well-powered reflective subcategories


Author: Rudolf-E. Hoffmann
Journal: Proc. Amer. Math. Soc. 90 (1984), 45-46
MSC: Primary 18A40
MathSciNet review: 722413
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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 ($ U$-small-indexed) limits, and

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


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0722413-1
PII: S 0002-9939(1984)0722413-1
Keywords: Reflective subcategory, co-well-powered category, epi-reflective hull
Article copyright: © Copyright 1984 American Mathematical Society