Functorial representation of closure operators
type: Item
instance of: scholarly article
zbMATH Open document ID: 0969.06003
author: Arturo Sangalli
author: Achille Achache
publication date: 2001-07-01T00:00:00Z
Mathematics Subject Classification ID: 06A15
Mathematics Subject Classification ID: 18B35
Mathematics Subject Classification ID: 18A40
Mathematics Subject Classification ID: 06B23
zbMATH DE Number: 1611748
zbMATH Keywords: category of residuated functions between complete lattices
zbMATH Keywords: endofunctor
zbMATH Keywords: closure operators
MaRDI profile type: Publication
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title: Functorial representation of closure operators
published in: Doklady Bolgarskoĭ Akademii Nauk
review text: 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 \(a\in \Omega\).
reviewed by: Vesselin Drensky
description: scientific article; zbMATH DE number 1611748