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
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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 (-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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