Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/178613
 Title: Proof verification in algebraic topology Author: Ripoll Echeveste, Xavier Director/Tutor: Casacuberta, Carles Keywords: Teoria de l'homotopiaTreballs de fi de grauÀlgebra homològicaLògica informàticaHomotopy theoryBachelor's thesisHomological algebraComputer 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

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