Amb motiu del tancament d'estiu, la validació de documents es reprendrà a partir del 28 d'agost de 2026. Disculpeu les molèsties.
Con motivo del cierre de verano, la validación de documentos se reanudará a partir del 28 de agosto de 2026. Disculpad las molestias
Due to the summer closure, document validation will resume starting August 28, 2026. We apologize for any inconvenience.

Document type

Bachelor thesis

Publication date

Publication license

cc-by-nc-nd (c) Jan McGarry Furriol, 2020
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/177842

Homotopical realizations of infinity Groupoids

Journal Title

Director/Tutor

Journal ISSN

Volume Title

Related resource

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.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Carles Casacuberta

Citation

Citation

MCGARRY FURRIOL, Jan. Homotopical realizations of infinity Groupoids. [consulted: 14 of August of 2026]. Available at: https://hdl.handle.net/2445/177842

Export metadata

JSON - METS

Share record