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dc.contributor.advisorÜnlü, Özgün
dc.contributor.authorErdal, Mehmet Akif
dc.date.accessioned2017-01-24T11:07:44Z
dc.date.available2017-01-24T11:07:44Z
dc.date.copyright2016-12
dc.date.issued2017-01
dc.date.submitted2017-01-18
dc.identifier.urihttp://hdl.handle.net/11693/32615
dc.descriptionCataloged from PDF version of article.en_US
dc.descriptionThesis (Ph.D.): Bilkent University, Department of Mathematics, İhsan Doğramacı Bilkent University, 2016.en_US
dc.descriptionIncludes bibliographical references (leaves 95-97).en_US
dc.description.abstractWe study actions of monoids and monoidal categories, and their relations with (co)homology theories. We start by discussing actions of monoids via bi-actions. We show that there is a well-defined functorial reverse action when a monoid action is given, which corresponds to acting by the inverses for group actions. We use this reverse actions to construct a homotopical structure on the category of monoid actions, which allow us to build the Burnside ring of a monoid. Then, we study categorifications of the previously introduced notions. In particular, we study actions of monoidal categories on categories and show that the ideas of action reversing of monoid actions extends to actions of monoidal categories. We use the reverse action for actions of monoidal categories, along with homotopy theory, to define homology, cohomology, homotopy and cohomotopy theories graded over monoidal categories. We show that most of the existing theories fits into our setting; and thus, we unify the existing definitions of these theories. Finally, we construct the spectral sequences for the theories graded over monoidal categories, which are the strongest tools for computation of cohomology and homotopy theories in existence.en_US
dc.description.statementofresponsibilityby Mehmet Akif Erdal.en_US
dc.format.extentviii, 97 leaves.en_US
dc.language.isoEnglishen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectMonoiden_US
dc.subjectMonoidal categoryen_US
dc.subjectActionen_US
dc.subjectReversilityen_US
dc.subjectBurnside ringen_US
dc.subjectStabilizationen_US
dc.subject(co)homologyen_US
dc.subject(co)homotopyen_US
dc.subjectSpectral sequenceen_US
dc.titleMonoid actions, their categorification and applicationsen_US
dc.title.alternativeMonoid etkileri, kategorifikasyonları ve uygulamalarıen_US
dc.typeThesisen_US
dc.departmentDepartment of Mathematicsen_US
dc.publisherBilkent Universityen_US
dc.description.degreePh.D.en_US
dc.identifier.itemidB147442
dc.embargo.release2017-12-28


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