2026-04-17T12:54:49Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/1077352025-07-22T17:16:24Zcom_2072_1033col_2072_452951

A brief introduction to synthetic differential geometry Pérez Scornik, Gaspar Universitat Politècnica de Catalunya. Departament de Matemàtiques Gràcia Sabaté, Francesc Xavier Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de categories; àlgebra homològica Categories (Mathematics) Synthetic Differential Geometry Smooth Toposes Smooth Manifolds Intuitionistic Logic Categories (Matemàtica) Classificació AMS::18 Category theory; homological algebra::18F Categories and geometry The 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). 2017-09 Bachelor thesis https://hdl.handle.net/2117/107735 FME-1543 eng http://creativecommons.org/licenses/by-nc-sa/3.0/es/ Open Access application/pdf Universitat Politècnica de Catalunya