Casacuberta, CarlesMcGarry Furriol, Jan2021-06-012021-06-012020-06-22https://hdl.handle.net/2445/177842Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Carles Casacuberta[en] Grothendieck’s homotopy hypothesis asserts that the study of homotopy types of topological spaces is equivalent to the study of $\infty$-groupoids, illustrating how important ideas in higher category theory stem from basic homotopical concepts. In practice there are distinct models for $\infty$-groupoids, and providing a proof of the homotopy hypothesis is a test for the suitability of any such model. In this thesis, we give a proof of the homotopy hypothesis using topological categories (i.e., categories enriched over topological spaces) as models for $\infty$-groupoids. In the same context, we propose a manageable model for the fundamental $\infty$-groupoids of a topological space.56 p.application/pdfengcc-by-nc-nd (c) Jan McGarry Furriol, 2020http://creativecommons.org/licenses/by-nc-nd/3.0/es/Categories (Matemàtica)Treballs de fi de grauTeoria de l'homotopiaGrupoidesCategories (Mathematics)Bachelor's thesesHomotopy theoryGroupoidsinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess