# name
Homotopical realizations of infinity Groupoids

# metadata.dc.description[].value
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Carles Casacuberta

# metadata.dc.description.abstract[].value
[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.

# metadata.dc.rights[].value
cc-by-nc-nd (c) Jan McGarry Furriol, 2020

# metadata.dc.source[].value
Treballs Finals de Grau (TFG) - Matemàtiques

# metadata.dc.title[].value
Homotopical realizations of infinity Groupoids