@article {
author = {Keshvardoost, Khadijeh and Mahmoudi, Mojgan},
title = {Separated finitely supported $Cb$-sets},
journal = {Categories and General Algebraic Structures with Applications},
volume = {13},
number = {1},
pages = {55-82},
year = {2020},
publisher = {Shahid Beheshti University},
issn = {2345-5853},
eissn = {2345-5861},
doi = {10.29252/cgasa.13.1.55},
abstract = {The monoid $Cb$ of name substitutions and the notion of finitely supported $Cb$-sets introduced by Pitts as a generalization of nominal sets. A simple finitely supported $Cb$-set is a one point extension of a cyclic nominal set. The support map of a simple finitely supported $Cb$-set is an injective map. Also, for every two distinct elements of a simple finitely supported $Cb$-set, there exists an element of the monoid $Cb$ which separates them by making just one of them into an element with the empty support.In this paper, we generalize these properties of simple finitely supported $Cb$-sets by modifying slightly the notion of the support map; defining the notion of $\mathsf{2}$-equivariant support map; and introducing the notions of s-separated and z-separated finitely supported $Cb$-sets. We show that the notions of s-separated and z-separated coincide for a finitely supported $Cb$-set whose support map is $\mathsf{2}$-equivariant. Among other results, we find a characterization of simple s-separated (or z-separated) finitely supported $Cb$-sets. Finally, we show that some subcategories of finitely supported $Cb$-sets with injective equivariant maps which constructed applying the defined notions are reflective.},
keywords = {Finitely supported $Cb$-sets,nominal set,$S$-set,support,simple},
url = {https://cgasa.sbu.ac.ir/article_87413.html},
eprint = {https://cgasa.sbu.ac.ir/article_87413_0b1bd3b91cc24e487df84a5e89e77f28.pdf}
}