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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Monofunctors as reflectors


Author: Claus Michael Ringel
Journal: Trans. Amer. Math. Soc. 161 (1971), 293-306
MSC: Primary 18A40
DOI: https://doi.org/10.1090/S0002-9947-1971-0292907-X
MathSciNet review: 0292907
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Abstract: In a well-powered and co-well-powered complete category $ \mathcal{K}$ with weak amalgamations, the class M of all reflective subcategories with a monofunctor as reflector forms a complete lattice; the limit-closure of the union of any class of elements of M belongs to M. If $ \mathcal{K}$ has injective envelopes, then the set-theoretical intersection of any class of elements of M belongs to M.


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DOI: https://doi.org/10.1090/S0002-9947-1971-0292907-X
Keywords: Category with amalgamations, lattice of reflective subcategories, limit-closure of the injectives, injective envelope, locally minimal subcategories, locally maximal subcategories, torsion theories in a module category, Grothendieck topologies
Article copyright: © Copyright 1971 American Mathematical Society

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