%0 Journal Article
%T Finitely presentable objects in ${\rm(}Cb\text{-}{\bf Sets}{\rm)}_{_{\rm fs}}$
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Haddadi, Mahdieh
%A Keshvardoost, Khadijeh
%A Hosseinabadi, Aliyeh
%D 2024
%\ 07/01/2024
%V 21
%N 1
%P 175-209
%! Finitely presentable objects in ${\rm(}Cb\text{-}{\bf Sets}{\rm)}_{_{\rm fs}}$
%K Finitely supported $M$-sets
%K Finitely supported $Cb$-sets
%K nominal sets
%K finitely presentable $Cb$-sets
%R 10.48308/cgasa.2024.235466.1487
%X Pitts generalized nominal sets to finitely supported $Cb$-sets by utilizing the monoid $Cb$ of name substitutions instead of the monoid of finitary permutations over names. Finitely supported $Cb$-sets provide a framework for studying essential ideas of models of homotopy type theory at the level of convenient abstract categories. Here, the interplay of two separate categories of finitely supported actions of a submonoid of ${\rm End}(\mathbb {D})$, for some countably infinite set $\mathbb {D}$, over sets is first investigated. In particular, we specify the structure of free objects.Then, in the category of finitely supported $Cb$-sets, we characterize the finitely presentable objects and provide a generator in this category.
%U https://cgasa.sbu.ac.ir/article_104615_923d1567db715dc3f19bcc09398d001c.pdf