Semigroup Actions on Sets and the Burnside Ring

  title={Semigroup Actions on Sets and the Burnside Ring},
  author={Mehmet Akif Erdal and {\"O}zg{\"u}n {\"U}nl{\"u}},
  journal={Applied Categorical Structures},
In this paper we discuss some enlargements of the category of sets with semigroup actions and equivariant functions. We show that these enlarged categories possess two idempotent endofunctors. In the case of groups these enlarged categories are equivalent to the usual category of group actions and equivariant functions, and these idempotent endofunctors reverse a given action. For a general semigroup we show that these enlarged categories admit homotopical category structures defined by using… 
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