Maximum monoreflections |
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Authors: | Anthony W Hager Jorge Martinez |
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Institution: | (1) Department of Mathematics, Wesleyan University, 06459 Middletown, CT, USA;(2) Department of Mathematics, University of Florida, 32611 Gainesville, FL, USA |
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Abstract: | It is shown that, in a category with a specified class of monics and under some mild hypothesis,there is a monoreflection maximum among those whose reflection maps lie in . Thus, for example, any variety, and most SP-classes in a variety, have both amaximum monoreflection and amaximum essential reflection (which might be the same, but frequently aren't, and which might be the identity functor, but frequently aren't). And, for example, under some mild hypotheses, beneath each completion lies a maximum monoreflection, so that, for example, any category of rings has amaximum functorial ring of quotients. |
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Keywords: | Primary 18A40 Secondary 18A30 13B30 |
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