INJECTIVITY OF G-NOMINAL SETS

Abstract

In this paper, we consider injectivity for nominal sets, G-sets for a subgroup G of the group Perm(\(\mathbb{D}\)) of permutations on an infinite countable set \(\mathbb{D}\), with finitely supported elements.  Also, we study injectivity of nominal sets with respect to monomorphisms whose domains or codomains are single-orbit.  Furthermore, we define the category of G_C-sets, for finite subsets C of \(\mathbb{D}\), where G_C is the set of elements of G fixing the elements of C, and study injectivity in such categories.