El producto tensorial de conjuntos dendroidales

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Javier J. Gutiérrez Marín[en] The main goal of this project is to understand the tensor product operation in the category of dendroidals sets. To do so, we introduce the notion of shuffles between two trees, and show how they are used in order to describe the tensor product. We begin with a quick review about categories, functors and operads, focusing on the basic definitions and constructions. Then, we introduce the formalism of trees, its relation to coloured operads and the definition of the dendroidal category \Omega, which serves as the indexing category for defining dendroidal sets as a presheaf category. We also show how the dendroidal category \Omega extends the simplicial category \Delta via the inclusion of linear trees, and the relation between simplicial sets and dendroidal sets. Finally, we develop a Python algorithm that generates the complete set of shuffles between two trees and prints their planar representations