TY - JOUR
ID - 104615
TI - Finitely presentable objects in ${\rm(}Cb\text{-}{\bf Sets}{\rm)}_{_{\rm fs}}$
JO - Categories and General Algebraic Structures with Applications
JA - CGASA
LA - en
SN - 2345-5853
AU - Haddadi, Mahdieh
AU - Keshvardoost, Khadijeh
AU - Hosseinabadi, Aliyeh
AD - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran.
AD - Department of Mathematics, Velayat University, Iranshahr, Sistan and
Balochistan, Iran.
AD - Faculty of Mathematics, Statistics and Computer Sciences, Department of Mathematics, Semnan University, Semnan, Iran.
Y1 - 2024
PY - 2024
VL - 21
IS - 1
SP - 175
EP - 209
KW - Finitely supported $M$-sets
KW - Finitely supported $Cb$-sets
KW - nominal sets
KW - finitely presentable $Cb$-sets
DO - 10.48308/cgasa.2024.235466.1487
N2 - 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.
UR - https://cgasa.sbu.ac.ir/article_104615.html
L1 - https://cgasa.sbu.ac.ir/article_104615_923d1567db715dc3f19bcc09398d001c.pdf
ER -