Functorial representation of closure operators (Q2720948)

For a fixed set \(S\), the partially ordered set \(\Omega\) of all closure operators \(2^S\to 2^S\) of \(S\) may be given a structure of category with objects the closure operators \(a\) and arrows the inclusions \(a\subset b\). In a previous paper [\textit{A. A. Achache} and \textit{A. A. Sangalli}, Zb. Rad., Prir.-Mat. Fak., Univ. Novom Sadu, Ser. Mat. 18, No. 2, 111-116 (1988; Zbl 0712.06002)] the authors defined an endofunctor \(E_a:{\mathcal L}\to {\mathcal L}\) in the category of residuated functions between complete lattices. In the paper under review the authors define a functor: \(\Omega\to\text{ End}{\mathcal L}\) which associates \(E_a\) to \(a\in \Omega\).