Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/177842
Homotopical realizations of infinity Groupoids
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[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.
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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Carles Casacuberta
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MCGARRY FURRIOL, Jan. Homotopical realizations of infinity Groupoids. [consulted: 29 of September of 2026]. Available at: https://hdl.handle.net/2445/177842