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DC Field | Value | Language |
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dc.contributor.advisor | Casacuberta, Carles | - |
dc.contributor.author | Martínez Carpena, David | - |
dc.date.accessioned | 2020-06-10T09:03:47Z | - |
dc.date.available | 2020-06-10T09:03:47Z | - |
dc.date.issued | 2020-01-19 | - |
dc.identifier.uri | http://hdl.handle.net/2445/165004 | - |
dc.description | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Carles Casacuberta | ca |
dc.description.abstract | [en] Homotopy type theory is a branch of mathematics that emerged in the decade of 2010. The major novelties with respect to previous type theories are the association of types with $\infty$ -groupoids, Voevodsky’s univalence axiom, and higher-order inductive types. Higher- order inductive types allow certain objects to be defined, such as a circle or a torus, in a synthetic way. The first chapters of this work offer an introduction to homotopy type theory, focusing especially on understanding higher-order inductive types. Due to the short time elapsed since the advent of homotopy type theory, there are many open questions waiting to be answered. This work sets out a research direction motivated by one of these questions: how to find an appropriate definition of orientability which is meaningful for surfaces or, more generally, for manifolds. From the existing definition of a torus as a higher-order inductive type, we have studied an analogous definition of a Klein bottle, focusing on the fact that a torus is a two-sheeted covering of a Klein bottle. This work contains basic facts about coverings in homotopy type theory, as well as a few results that are relevant in the special case of the torus and the Klein bottle. | ca |
dc.format.extent | 56 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | cat | ca |
dc.rights | cc-by-nc-nd (c) David Martínez Carpena, 2020 | - |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | * |
dc.source | Treballs Finals de Grau (TFG) - Matemàtiques | - |
dc.subject.classification | Teoria de l'homotopia | ca |
dc.subject.classification | Treballs de fi de grau | - |
dc.subject.classification | Tor (Geometria) | ca |
dc.subject.classification | Àlgebra homològica | ca |
dc.subject.classification | Lògica informàtica | ca |
dc.subject.other | Homotopy theory | en |
dc.subject.other | Bachelor's theses | - |
dc.subject.other | Torus (Geometry) | en |
dc.subject.other | Homological algebra | en |
dc.subject.other | Computer logic | en |
dc.title | Teoria homotòpica de tipus | ca |
dc.type | info:eu-repo/semantics/bachelorThesis | ca |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
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File | Description | Size | Format | |
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165004.pdf | Memòria | 626.26 kB | Adobe PDF | View/Open |
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