Anzeige
Erschienen in:
30.08.2017 | Foundations
Free functor from the category of G-nominal sets to that of 01-G-nominal sets
Erschienen in: Soft Computing | Ausgabe 11/2018
EinloggenAktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Abstract
The category \(\mathbf{Nom}\), of all finitely supported G-sets, called G-nominal sets, where \(G=\mathrm{Perm}_{\mathrm{f}}({\mathbb {D}})\) is the group of all finitary permutations over a countable infinite set \({\mathbb {D}}\), is a subject of interest by both set theorists and computer scientists. The category 01-Nom, of all G-nominal sets equipped with the source and the target operations, was introduced by Pitts. He has shown that this category is isomorphic to the category of sets whose elements have a finite support property with respect to an action of the monoid Cb of name substitutions. The latter category is a coreflective subcategory of the category \(\mathbf{Set}^{Cb}\), of sets with the action of the monoid Cb. For a functorial relation between the categories \(\mathbf{Nom}\) and \(\mathbf{Set}^{Cb}\), we study the existence of the free objects in the category 01-Nom. More precisely, we construct the left adjoint to the forgetful functor from the category of 01-G-nominal sets to the category of G-nominal sets, where G is a suitable subgroup of the group of all permutations over a countable infinite set \({\mathbb {D}}\).