On Regular Closure Operators and Cowellpowered Subcategories

Details On Regular Closure Operators and Cowellpowered Subcategories On Regular Closure Operators and Cowellpowered Subcategories

2002-06-12

arxiv.org/abs/math/0206124v2

Mathematics

Category Theory

16 pages, LaTex, 11pt ps.file, Corrected and revised version. Submitted to : Comment. Math. Univ. Carolinae

Scientific paper

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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