{"id":38911,"date":"1998-04-12T00:00:00","date_gmt":"1998-04-12T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/algebra-homotopica-en-categorias-que-modelan-algebraicamente-espacios-no-conexos\/"},"modified":"1998-04-12T00:00:00","modified_gmt":"1998-04-12T00:00:00","slug":"algebra-homotopica-en-categorias-que-modelan-algebraicamente-espacios-no-conexos","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/algebra-homotopica-en-categorias-que-modelan-algebraicamente-espacios-no-conexos\/","title":{"rendered":"Algebra homotopica en categorias que modelan algebraicamente espacios no conexos."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Raquel Osorio Blanco <\/strong><\/h2>\n<p>La memoria se enmarca dentro de lo que se conoce como teor\u00eda de homotop\u00eda abstracta, en la l\u00ednea desarrollada por quillen. El objetivo fundamental es obtener en la categor\u00eda de grupoides simpliciales, con conjunto de objetos constante c y en ciertas subcategor\u00edas suyas, diferentes estructuras de modelos y estudiar entonces las correspondientes teor\u00edas de homotop\u00eda.  la memoria se divide en cuatro cap\u00edtulos. El primero de ellos est\u00e1 destinado a introducir los conceptos y resultados fundamentales que se utilizan en la memoria. El objetivo fundamental del cap\u00edtulo 2 es dar una demostraci\u00f3n de que c es una categor\u00eda de modelos cerrada con la estructura propuesta por dwyer-kan en su trabajo homotopy theory and simplicial groupoids, as\u00ed como la equiValencia de la categor\u00eda de homotop\u00eda resultante y la categor\u00eda de conjuntos simpliciales, con su estructura usual, y en consecuencia con la categor\u00eda de espacios topol\u00f3gicos. esta equiValencia no es s\u00f3lo de categor\u00edas, sino tambi\u00e9n de teor\u00edas de homotop\u00eda, esto es, preserva objeto cilindro, espacio arco y sucesiones fibraci\u00f3n y cofibraci\u00f3n. Se describen expl\u00edcitamente el espacio de arcos y el objeto cilindro, resultando que las homotop\u00edas entre morfismos introducidos en la memoria, quedan caracterizados, como es usual, por los objetos anteriores.  en el cap\u00edtulo 3 se estudian otras estructuras de modelos para c. As\u00ed para cada n-&gt;0, apoy\u00e1ndose en la estructura anterior y mediante el uso del funtor coesqueleto, se definen los conceptos de n-(co)-fibraci\u00f3n y n-equiValencia d\u00e9bil, obteniendo as\u00ed una estructura, la n-estructura, con la que c es tambi\u00e9n una categor\u00eda de modelos cerrada. Se estudia entonces la teor\u00eda de homotop\u00eda resultante y el cap\u00edtulo finaliza comparando dicha teor\u00eda de homotop\u00eda con otras existentes. En particular, se concluye que la categor\u00eda de homotop\u00eda con la n-estructura es equivalente a la categor\u00eda de homotop\u00eda de cw-c<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Algebra homotopica en categorias que modelan algebraicamente espacios no conexos.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Algebra homotopica en categorias que modelan algebraicamente espacios no conexos. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Raquel Osorio Blanco <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Granada<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 04\/12\/1998<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Jes\u00fas Garc\u00eda Miranda<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: alfredo Rodriguez grandjean lopez varcarcel <\/li>\n<li>carles Casacuberta verg\u00e9s (vocal)<\/li>\n<li>Antonio Mart\u00ednez  cegarra (vocal)<\/li>\n<li>Luis Javier Hernandez paricio (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Raquel Osorio Blanco La memoria se enmarca dentro de lo que se conoce como teor\u00eda de homotop\u00eda [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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