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On Regular Closure Operators and Cowellpowered Subcategories

Vishvajit V. S. Gautam
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Abstract

Many Properties of a category X, as for instance the existence of an adjoint or a factorization system, are a consequence of the cowellpoweredness of X. In the absence of cowellpoweredness, for general results, fairly strong assumption on the category are needed. This paper provides a number of novel and useful observations to tackle the cowellpoweredness problem of subcategories by means of regular closure operators. Our exposition focusses on the question when two subcategories A and B induce the same regular closure operators, then information about (non)-cowellpoweredness of A may be gained from corresponding property of B, and vice versa.

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Vishvajit V. S. Gautam. 2002-08-13. On Regular Closure Operators and Cowellpowered Subcategories. https://arxiv.org/abs/math/0206124

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