Monofunctors as reflectors

Ringel, Claus Michael

doi:10.1090/S0002-9947-1971-0292907-X

Monofunctors as reflectors
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by Claus Michael Ringel

Trans. Amer. Math. Soc. 161 (1971), 293-306

DOI: https://doi.org/10.1090/S0002-9947-1971-0292907-X

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Abstract:

In a well-powered and co-well-powered complete category $\mathcal {K}$ with weak amalgamations, the class $\mathbfit {M}$ 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 $\mathbfit {M}$ belongs to $\mathbfit {M}$. If $\mathcal {K}$ has injective envelopes, then the set-theoretical intersection of any class of elements of $\mathbfit {M}$ belongs to $\mathbfit {M}$.

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Séminaire géométrie algébrique

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