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Title: Homotopical realizations of infinity Groupoids
Author: McGarry Furriol, Jan
Director/Tutor: Casacuberta, Carles
Keywords: Categories (Matemàtica)
Treballs de fi de grau
Teoria de l'homotopia
Categories (Mathematics)
Bachelor's thesis
Homotopy theory
Issue Date: 22-Jun-2020
Abstract: [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.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Carles Casacuberta
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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