dc.contributor.author Erdal, Mehmet Akif en_US dc.contributor.author Ünlü, Özgün en_US dc.date.accessioned 2019-01-25T05:42:11Z dc.date.available 2019-01-25T05:42:11Z dc.date.issued 2018 en_US dc.identifier.issn 0927-2852 dc.identifier.uri http://hdl.handle.net/11693/48336 dc.description.abstract In this paper we discuss some enlargements of the category of sets with semigroup en_US 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 these endofunctors and show that up to homotopy these categories are equivalent to the usual category of sets with semigroup actions. We finally construct the Burnside ring of a monoid by using homotopical structure of these categories, so that when the monoid is a group this definition agrees with the usual definition, and we show that when the monoid is commutative, its Burnside ring is equivalent to the Burnside ring of its Gr¨othendieck group. dc.language.iso English en_US dc.source.title Applied Categorical Structures en_US dc.relation.isversionof https://doi.org/10.1007/s10485-016-9477-4 en_US dc.subject Semigroup actions en_US dc.subject Monoid actions en_US dc.subject Reverse actions en_US dc.subject Homotopical category en_US dc.subject Burnside ring en_US dc.subject 16W22 en_US dc.subject 20M20 en_US dc.subject 20M35 en_US dc.subject 55U35 en_US dc.title Semigroup actions on sets and the burnside ring en_US dc.type Article en_US dc.department Department of Mathematics en_US dc.citation.spage 7 en_US dc.citation.epage 28 en_US dc.citation.volumeNumber 26 en_US dc.citation.issueNumber 1 en_US dc.identifier.doi 10.1007/s10485-016-9477-4 en_US dc.publisher Springer Science en_US dc.contributor.bilkentauthor Erdal, Mehmet Akif dc.contributor.bilkentauthor Ünlü, Özgün dc.identifier.eissn 1572-9095
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