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Transactions of the American Mathematical Society

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



Coreflective subcategories

Authors: Horst Herrlich and George E. Strecker
Journal: Trans. Amer. Math. Soc. 157 (1971), 205-226
MSC: Primary 18.10
MathSciNet review: 0280561
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Abstract: General morphism factorization criteria are used to investigate categorical reflections and coreflections, and in particular epi-reflections and monocoreflections. It is shown that for most categories with ``reasonable'' smallness and completeness conditions, each coreflection can be ``split'' into the composition of two mono-coreflections and that under these conditions mono-coreflective subcategories can be characterized as those which are closed under the formation of coproducts and extremal quotient objects. The relationship of reflectivity to closure under limits is investigated as well as coreflections in categories which have ``enough'' constant morphisms.

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Keywords: Coreflective subcategory, mono-coreflection, reflective subcategory, epi-reflection, epi-mono factorization, extremal epimorphism, extremal monomorphism
Article copyright: © Copyright 1971 American Mathematical Society