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dc.contributorGràcia Sabaté, Francesc Xavier
dc.contributor.authorPérez Scornik, Gaspar
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.description.abstractThe goal of this thesis is to explore the basic axiomatic theory of Syn- thetic Differential Geometry (SDG). This field aims to put the study of smooth manifolds, and geometry therein, in a topos-theoretic framework. Though the full depth of application and consequences of SDG require knowledge of topos theory to comprehend, a large part of the theory can be appreciated with only some notions of basic category theory (as well as with a standard undergraduate mathematics syllabus). In this work we look at this part of SDG, called the axiomatic the- ory because it is indeed developed axiomatically. Specifically, under the axiomatic theory of SDG we look at differential calculus, then manifolds (their analogue in SDG), vector bundles (the tangent bundle as a particular case), and vector fields (and Lie algebras thereof).
dc.publisherUniversitat Politècnica de Catalunya
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de categories; àlgebra homològica
dc.subject.lcshCategories (Mathematics)
dc.subject.otherSynthetic Differential Geometry
dc.subject.otherSmooth Toposes
dc.subject.otherSmooth Manifolds
dc.subject.otherIntuitionistic Logic
dc.titleA brief introduction to synthetic differential geometry
dc.typeBachelor thesis
dc.subject.lemacCategories (Matemàtica)
dc.subject.amsClassificació AMS::18 Category theory; homological algebra::18F Categories and geometry
dc.rights.accessOpen Access
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística
dc.audience.degreeGRAU EN MATEMÀTIQUES (Pla 2009)

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