From model to quasi-categories

Detalhes bibliográficos
Autor(a) principal: Daniel de Souza Plácido Teixeira
Data de Publicação: 2022
Tipo de documento: Dissertação
Idioma: eng
Título da fonte: Repositório Institucional da UFMG
Texto Completo: http://hdl.handle.net/1843/47395
Resumo: This dissertation is a humble introduction to important tools of abstract homotopy theory: model categories and ∞-categories (through quasicategories). The first part of the text presents these frameworks, connecting them with various topics from category theory, classical homotopy theory and homological algebra. In the second part, we use these tools to study issues internal to homotopy theory itself, and to compare these two languages that we study through simplicial localization.
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spelling Raphael Campos Drumondhttp://lattes.cnpq.br/6034594218861618Yuri Ximenes Martinshttp://lattes.cnpq.br/7703153488734239Maru SarazolaViktor Bekkerthttp://lattes.cnpq.br/1939411434322215Daniel de Souza Plácido Teixeira2022-11-22T18:31:21Z2022-11-22T18:31:21Z2022-02-22http://hdl.handle.net/1843/47395This dissertation is a humble introduction to important tools of abstract homotopy theory: model categories and ∞-categories (through quasicategories). The first part of the text presents these frameworks, connecting them with various topics from category theory, classical homotopy theory and homological algebra. In the second part, we use these tools to study issues internal to homotopy theory itself, and to compare these two languages that we study through simplicial localization.Esta dissertação é uma humilde introdução a grandes ferramentas da teoria da homotopia abstrata: categorias modelo e ∞-categorias (através de quasicategorias). A primeira parte do texto apresenta estas estruturas, conectando com diversos tópicos de teoria das categorias, teoria da homotopia clássica e álgebra homológica. Na segunda parte, usamos este ferramental para estudar questões internas à própria teoria da homotopia, e para comparar essas duas linguagens que estudamos através da localização simplicial.CNPq - Conselho Nacional de Desenvolvimento Científico e TecnológicoengUniversidade Federal de Minas GeraisPrograma de Pós-Graduação em MatemáticaUFMGBrasilICX - DEPARTAMENTO DE MATEMÁTICAhttp://creativecommons.org/licenses/by-sa/3.0/pt/info:eu-repo/semantics/openAccessMatemática – TesesCategorias (Matemática) – TesesTeoria da homotopia –TesesTopologia algébrica – TesesÁlgebra Homológica – TesesCategory TheoryHomotopy TheoryAlgebraic TopologyHomological AlgebraFrom model to quasi-categoriesDe categorias modelo a quasi-categoriasinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMGCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-81031https://repositorio.ufmg.br/bitstream/1843/47395/3/license_rdf5dda753f5b57b1020a56e348e443aa73MD53LICENSElicense.txtlicense.txttext/plain; charset=utf-82118https://repositorio.ufmg.br/bitstream/1843/47395/4/license.txtcda590c95a0b51b4d15f60c9642ca272MD54ORIGINALdissertação_merged (1)_organized.pdfdissertação_merged (1)_organized.pdfapplication/pdf1011591https://repositorio.ufmg.br/bitstream/1843/47395/1/disserta%c3%a7%c3%a3o_merged%20%281%29_organized.pdf7dd364e02582d5cea42709eb28774621MD511843/473952022-11-22 15:31:22.338oai:repositorio.ufmg.br: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ório de PublicaçõesPUBhttps://repositorio.ufmg.br/oaiopendoar:2022-11-22T18:31:22Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false
dc.title.pt_BR.fl_str_mv From model to quasi-categories
dc.title.alternative.pt_BR.fl_str_mv De categorias modelo a quasi-categorias
title From model to quasi-categories
spellingShingle From model to quasi-categories
Daniel de Souza Plácido Teixeira
Category Theory
Homotopy Theory
Algebraic Topology
Homological Algebra
Matemática – Teses
Categorias (Matemática) – Teses
Teoria da homotopia –Teses
Topologia algébrica – Teses
Álgebra Homológica – Teses
title_short From model to quasi-categories
title_full From model to quasi-categories
title_fullStr From model to quasi-categories
title_full_unstemmed From model to quasi-categories
title_sort From model to quasi-categories
author Daniel de Souza Plácido Teixeira
author_facet Daniel de Souza Plácido Teixeira
author_role author
dc.contributor.advisor1.fl_str_mv Raphael Campos Drumond
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/6034594218861618
dc.contributor.advisor2.fl_str_mv Yuri Ximenes Martins
dc.contributor.advisor2Lattes.fl_str_mv http://lattes.cnpq.br/7703153488734239
dc.contributor.referee1.fl_str_mv Maru Sarazola
dc.contributor.referee2.fl_str_mv Viktor Bekkert
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/1939411434322215
dc.contributor.author.fl_str_mv Daniel de Souza Plácido Teixeira
contributor_str_mv Raphael Campos Drumond
Yuri Ximenes Martins
Maru Sarazola
Viktor Bekkert
dc.subject.por.fl_str_mv Category Theory
Homotopy Theory
Algebraic Topology
Homological Algebra
topic Category Theory
Homotopy Theory
Algebraic Topology
Homological Algebra
Matemática – Teses
Categorias (Matemática) – Teses
Teoria da homotopia –Teses
Topologia algébrica – Teses
Álgebra Homológica – Teses
dc.subject.other.pt_BR.fl_str_mv Matemática – Teses
Categorias (Matemática) – Teses
Teoria da homotopia –Teses
Topologia algébrica – Teses
Álgebra Homológica – Teses
description This dissertation is a humble introduction to important tools of abstract homotopy theory: model categories and ∞-categories (through quasicategories). The first part of the text presents these frameworks, connecting them with various topics from category theory, classical homotopy theory and homological algebra. In the second part, we use these tools to study issues internal to homotopy theory itself, and to compare these two languages that we study through simplicial localization.
publishDate 2022
dc.date.accessioned.fl_str_mv 2022-11-22T18:31:21Z
dc.date.available.fl_str_mv 2022-11-22T18:31:21Z
dc.date.issued.fl_str_mv 2022-02-22
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/1843/47395
url http://hdl.handle.net/1843/47395
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv http://creativecommons.org/licenses/by-sa/3.0/pt/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-sa/3.0/pt/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Universidade Federal de Minas Gerais
dc.publisher.program.fl_str_mv Programa de Pós-Graduação em Matemática
dc.publisher.initials.fl_str_mv UFMG
dc.publisher.country.fl_str_mv Brasil
dc.publisher.department.fl_str_mv ICX - DEPARTAMENTO DE MATEMÁTICA
publisher.none.fl_str_mv Universidade Federal de Minas Gerais
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFMG
instname:Universidade Federal de Minas Gerais (UFMG)
instacron:UFMG
instname_str Universidade Federal de Minas Gerais (UFMG)
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