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Les algèbres de Hopf dans les catégories monoïdales tressées

Aït Said, Amine
(2021)

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AïtSaid_64751400_2021.pdf
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Details

Supervisors
Gran, Marino ; Sterck, Florence
Faculty
Faculté des sciences
Degree label
Master [120] en sciences mathématiques, à finalité approfondie
Abstract
enThe objective of this thesis is to construct and study Hopf algebras in braided monoidal categories. To achieve this goal, we started by defining monoidal categories and by studying the relation between a monoidal category and a strict monoidal category. Then, we constructed algebras and coalgebras in monoidal categories. To them, we added an additional structure to arrive at the braided monoidal categories. By means of an example, we discovered that there are objects that are both an algebra and a coalgebra, and this discovery allowed us to introduce the bialgebras. Afterwards, in the context of braided monoidal categories, we presented the bijection relation between the bialgebra structures on an algebra and the monoidal structures on the module category. Finally, all the results have been gathered in order to reach the goal, namely to define and analyze Hopf algebras in braided monoidal categories.