Ladra González, ManuelLinden, Tim Van derGarcía-Martínez, Xabier2018-02-062018-02-062017http://hdl.handle.net/10347/16431The objective of this dissertation is twofold: firstly to use categorical and algebraic methods to study homological properties of some of the aforementioned semi-abelian, non-associative structures and secondly to use categorical and algebraic methods to study categorical properties and provide categorical characterisations of some well-known algebraic structures. On one hand, the theory of universal central extensions together with the non-abelian tensor product will be studied and used to explicitly calculate some homology groups and some problems about universal enveloping algebras and actions will be solved. On the other hand, we will focus on giving categorical characterisations of some algebraic structures, such as a characterisation of groups amongst monoids, of cocommutative Hopf algebras amongst cocommutative bialgebras and of Lie algebras amongst alternating algebras.engEsta obra atópase baixo unha licenza internacional Creative Commons BY-NC-ND 4.0. Calquera forma de reprodución, distribución, comunicación pública ou transformación desta obra non incluída na licenza Creative Commons BY-NC-ND 4.0 só pode ser realizada coa autorización expresa dos titulares, salvo excepción prevista pola lei. Pode acceder Vde. ao texto completo da licenza nesta ligazón: https://creativecommons.org/licenses/by-nc-nd/4.0/deed.glhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.glCategorical algebraNon-associative algebrassemi-abelian categories(co)homology theoryMaterias::Investigación::12 Matemáticas::1201 Algebra::120112 Algebras no asociativasMaterias::Investigación::12 Matemáticas::1202 Análisis y análisis funcional::120203 Algebra y espacios de Banachdoctoral thesisopen access