Algebraic deformation of a monoidal category

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 dc.contributor.author Shrestha, Tej Bahadur dc.date.accessioned 2010-10-28T18:09:55Z dc.date.available 2010-10-28T18:09:55Z dc.date.issued 2010-10-28T18:09:55Z dc.identifier.uri http://hdl.handle.net/2097/6393 dc.description.abstract This dissertation begins the development of the deformation theorem of monoidal categories which accounts for the function that all en_US arrow-valued operations, composition, the arrow part of the monoidal product, and structural natural transformation are deformed. The first chapter is review of algebra deformation theory. It includes the Hochschild complex of an algebra, Gerstenhaber's deformation theory of rings and algebras, Yetter's deformation theory of a monoidal category, Gerstenhaber and Schack's bialgebra deformation theory and Markl and Shnider's deformation theory for Drinfel'd algebras. The second chapter examines deformations of a small $k$-linear monoidal category. It examines deformations beginning with a naive computational approach to discover that as in Markl and Shnider's theory for Drinfel'd algebras, deformations of monoidal categories are governed by the cohomology of a multicomplex. The standard results concerning first order deformations are established. Obstructions are shown to be cocycles in the special case of strict monoidal categories when one of composition or tensor or the associator is left undeformed. At the end there is a brief conclusion with conjectures. dc.language.iso en_US en_US dc.publisher Kansas State University en dc.subject Algebraic Deformation of a Monoidal Category en_US dc.subject Yetter complex and Hochschild complex of monoidal category en_US dc.title Algebraic deformation of a monoidal category en_US dc.type Dissertation en_US dc.description.degree Doctor of Philosophy en_US dc.description.level Doctoral en_US dc.description.department Department of Mathematics en_US dc.description.advisor David Yetter en_US dc.subject.umi Mathematics (0405) en_US dc.date.published 2010 en_US dc.date.graduationmonth December en_US
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