Semigroup actions on sets and the burnside ring

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buir.contributor.authorErdal, Mehmet Akif
buir.contributor.authorÜnlü, Özgün
dc.citation.epage28en_US
dc.citation.issueNumber1en_US
dc.citation.spage7en_US
dc.citation.volumeNumber26en_US
dc.contributor.authorErdal, Mehmet Akifen_US
dc.contributor.authorÜnlü, Özgünen_US
dc.date.accessioned2019-01-25T05:42:11Z
dc.date.available2019-01-25T05:42:11Z
dc.date.issued2018en_US
dc.departmentDepartment of Mathematicsen_US
dc.description.abstractIn 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 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.en_US
dc.description.provenanceSubmitted by Mandana Moftakhari (mandana.mir@bilkent.edu.tr) on 2019-01-25T05:42:11Z No. of bitstreams: 1 Semigroup_Actions_on_Sets_and_the_Burnside_Ring.pdf: 1106949 bytes, checksum: 14011b681b3f8cf1f912f6bda9e4aebb (MD5)en
dc.description.provenanceMade available in DSpace on 2019-01-25T05:42:11Z (GMT). No. of bitstreams: 1 Semigroup_Actions_on_Sets_and_the_Burnside_Ring.pdf: 1106949 bytes, checksum: 14011b681b3f8cf1f912f6bda9e4aebb (MD5) Previous issue date: 2016-12-24en
dc.identifier.doi10.1007/s10485-016-9477-4en_US
dc.identifier.eissn1572-9095
dc.identifier.issn0927-2852
dc.identifier.urihttp://hdl.handle.net/11693/48336
dc.language.isoEnglishen_US
dc.publisherSpringer Scienceen_US
dc.relation.isversionofhttps://doi.org/10.1007/s10485-016-9477-4en_US
dc.source.titleApplied Categorical Structuresen_US
dc.subjectSemigroup actionsen_US
dc.subjectMonoid actionsen_US
dc.subjectReverse actionsen_US
dc.subjectHomotopical categoryen_US
dc.subjectBurnside ringen_US
dc.subject16W22en_US
dc.subject20M20en_US
dc.subject20M35en_US
dc.subject55U35en_US
dc.titleSemigroup actions on sets and the burnside ringen_US
dc.typeArticleen_US

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