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Characteristic triangles of closure operators with applications in general algebra. (English) Zbl 1209.08001

The aim of this paper is to investigate groups and their weak congruence lattices in the abstract setting of lattices \(L\) with (local) closure operators \(C\) in the categorical sense, where \(L\) is regarded as a small category and \(C\) is a family of closure maps on the principal ideals of \(L\). A useful tool for structural investigations of such lattices with closure is the so-called characteristic triangle, a certain substructure of the square \( L^2\).

MSC:

08A30 Subalgebras, congruence relations
06B05 Structure theory of lattices
18B35 Preorders, orders, domains and lattices (viewed as categories)
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