Ladra González, ManuelFernández Fariña, Alejandro2021-07-152021-07-152021http://hdl.handle.net/10347/26581This thesis is devoted to the study of braidings in different mathematical contexts, as well as in a deeper analysis of the Loday-Pirashvili category. We will study the notion of braidings for crossed modules and internal categories in the cases of groups, associative algebras, Lie algebras and Leibniz algebras, showing the equivalence between the respective categories. We will also study universal central extensions in the category of braided crossed modules of Lie algebras. Finally, we will show how to generalize the Loday-Pirashvili category. With that construction, we will exhibit a generalization of the relationship between Lie and Leibniz objects.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Braided categoryCrossed ModuleLie AlgebraLeibniz Algebrauniversal central extensionLoday-Pirashvili categoryMaterias::Investigación::12 Matemáticas::1201 Algebra::120103 Teoría de categoríasMaterias::Investigación::12 Matemáticas::1201 Algebra::120109 Algebra de LieMaterias::Investigación::12 Matemáticas::1201 Algebra::120112 Algebras no asociativasdoctoral thesisopen access