Opetopes, rewriting, and koszulity
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Thesis Description :

Opetopes were originally introduced by as an algebraic structure to describe compositions and coherence laws in weak higher dimensional categories. They differ from other shapes (such as globular or simplicial) by their higher tree structure.
However, their recursive nature makes them difficult to manipulate, and the first aim of this thesis is to provide results and techniques for more convenient usage. Then, we study applications of this theory, mainly directed towards higher rewriting theory, and a generalization of the operadic Koszul duality to the operopic setting.