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pro vyhledávání: '"Tenório, Ana Luiza"'
We expand \v{C}ech cohomology of a topological space $X$ with values in a presheaf on $X$ to \v{C}ech cohomology of a commutative ring with unity $R$ with values in a presheaf on $R$. The strategy is to observe that both the set of open subsets of $X
Externí odkaz:
http://arxiv.org/abs/2404.12884
Autor:
Tenório, Ana Luiza, Mariano, Hugo Luiz
In this paper, we present a generalization of Grothendieck pretopologies -- suited for semicartesian categories with equalizers $C$ -- leading to a closed monoidal category of sheaves, instead of closed cartesian category. This is proved through a di
Externí odkaz:
http://arxiv.org/abs/2404.12313
In this paper we study categorical properties of the category of (abelian) hypergroups that leads to the notion of hyper-quasipreadditive and hyper-quasiabelian categories. Our goal is to create a path towards a general theory of homological algebra
Externí odkaz:
http://arxiv.org/abs/2205.02362
In this paper, we introduce a new definition of sheaves on semicartesian quantales, providing first examples and categorical properties. We note that our sheaves are similar to the standard definition of a sheaf on a locale, however, we prove in that
Externí odkaz:
http://arxiv.org/abs/2204.08351
Autor:
Tenorio, Ana Luiza, Mariano, Hugo Luiz
In this survey paper, we present \v{C}ech and sheaf cohomologies -- themes that were presented by Koszul in University of S\~ao Paulo during his visit in the late 1950s -- we present expansions for categories of generalized sheaves (i.e, Grothendieck
Externí odkaz:
http://arxiv.org/abs/2008.10677
Akademický článek
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We extend the classic definition of sheaves on locales introducing an original notion of sheaves on semicartesian quantales. We show that the resulting category and the category of sheaves on locales share similar categorical properties, and discuss
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9f400aea53e347784a017883ed036ae2
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