Algebraic deformation of a monoidal category
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Abstract
This dissertation begins the development of the deformation theorem of monoidal categories which accounts for the function that all
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