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Master's Dissertation
DOI
Document
Author
Full name
Ana Luiza da Conceição Tenorio
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2019
Supervisor
Committee
Mariano, Hugo Luiz (President)
Arndt, Peter
Pedra, Walter Alberto de Siqueira
Title in Portuguese
Álgebra homológica em topos
Keywords in Portuguese
Álgebra homológica
Categorias abelianas
Feixes
Topos de Grothendieck
Abstract in Portuguese
O objetivo dessa Dissertação é detalhar resultados conhecidos de Cohomologia em Topos de Grothendieck. Para isso, apresentamos a Álgebra Homológica em seu contexto mais geral, através de Categorias Abelianas, introduzindo as principais noções da área como funtores derivados e sequências espectrais. Desenvolvemos também o essencial da Teoria de Topos, explicando como um topos de Grothendieck surge como uma certa generalização dos feixes de conjuntos e fornecemos aspectos lógicos dos topos elementares. Focamos sobretudo nos Topos de Grothendieck pois a partir deles podemos construir categorias abelianas com suficientes injetivos, as quais são necessárias para expressar os grupos de cohomologia.
Title in English
Homological algebra in toposes
Keywords in English
Abelian categories
Grothendieck topos
Homological algebra
Sheaves
Abstract in English
The final objective of this Dissertation is to detail known results of Cohomology in Grothendieck Topos. For this, we present Homological Algebra in its more general context, through Abelian Categories, introducing the main notions of the area as derived functors and spectral sequences. We also develop the basics of the Topos Theory, explaining how a Grothendieck Topos arises as a certain generalization of sheafs and we provide logical aspects of the elementary topos. We focus mainly in the Grothendieck Topos because from them we can construct abelians categories.
 
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Publishing Date
2019-04-30
 
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