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http://hdl.handle.net/2445/178613
Title: | Proof verification in algebraic topology |
Author: | Ripoll Echeveste, Xavier |
Director/Tutor: | Casacuberta, Carles |
Keywords: | Teoria de l'homotopia Treballs de fi de grau Àlgebra homològica Lògica informàtica Homotopy theory Bachelor's theses Homological algebra Computer logic |
Issue Date: | 21-Jun-2020 |
Abstract: | [en] Homotopy type theory is a relatively new field which results from the surprising blend of algebraic topology (homotopy) and type theory (type), that tries to serve as a theoretical base for theorem-proving software. This setting is particularly suitable for synthetic homotopy theory. In this work, we describe how the programming language Agda can be used for proof verification, by examining the construction of the fundamental group of the circle $\mathbb{S}^{1}$. Then, trying to obtain the fundamental group of the real projective plane $\mathbb{R} \mathrm{P}^{2}$, we end up exploring a new construction of $\mathbb{R} \mathrm{P}^{2}$ as a higher inductive type. |
Note: | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Carles Casacuberta |
URI: | http://hdl.handle.net/2445/178613 |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques Treballs Finals de Grau (TFG) - Enginyeria Informàtica |
Files in This Item:
File | Description | Size | Format | |
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codi.zip | Codi font | 111.66 kB | zip | View/Open |
tfg_ripoll_echeveste_xavier.pdf | Memòria | 460.08 kB | Adobe PDF | View/Open |
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