Finitely presentable objects in ${\rm(}Cb\text{-}{\bf Sets}{\rm)}_{_{\rm fs}}$

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran.

2 Department of Mathematics, Velayat University, Iranshahr, Sistan and Balochistan, Iran.

3 Faculty of Mathematics, Statistics and Computer Sciences, Department of Mathematics, Semnan University, Semnan, Iran.

Abstract

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.

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References

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Categories and General Algebraic Structures with Applications
Volume 21, Issue 1
July 2024
Pages 175-209

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