dc.contributor.advisor Ünlü, Özgün dc.contributor.author Erdal, Mehmet Akif dc.date.accessioned 2017-01-24T11:07:44Z dc.date.available 2017-01-24T11:07:44Z dc.date.copyright 2016-12 dc.date.issued 2017-01 dc.date.submitted 2017-01-18 dc.identifier.uri http://hdl.handle.net/11693/32615 dc.description Cataloged from PDF version of article. en_US dc.description Thesis (Ph.D.): Bilkent University, Department of Mathematics, İhsan Doğramacı Bilkent University, 2016. en_US dc.description Includes bibliographical references (leaves 95-97). en_US dc.description.abstract We 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.statementofresponsibility by Mehmet Akif Erdal. en_US dc.format.extent viii, 97 leaves. en_US dc.language.iso English en_US dc.rights info:eu-repo/semantics/openAccess en_US dc.subject Monoid en_US dc.subject Monoidal category en_US dc.subject Action en_US dc.subject Reversility en_US dc.subject Burnside ring en_US dc.subject Stabilization en_US dc.subject (co)homology en_US dc.subject (co)homotopy en_US dc.subject Spectral sequence en_US dc.title Monoid actions, their categorification and applications en_US dc.title.alternative Monoid etkileri, kategorifikasyonları ve uygulamaları en_US dc.type Thesis en_US dc.department Department of Mathematics en_US dc.publisher Bilkent University en_US dc.description.degree Ph.D. en_US dc.identifier.itemid B147442 dc.embargo.release 2017-12-28
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