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math.CT2025
The Category of Hypergroups: seeking for a generalized version of Abelian Categories
Kaique Matias de Andrade Roberto, Ana Luiza Tenório
In this paper we study categorical properties of the category of abelian hypergroups that leads to the notion of hyper (almost) preadditive and hyper (almost) abelian categories. O…
math.CT2024
Expanding Äech cohomology for quantales
Ana Luiza Tenório, Peter Arndt, Hugo Luiz Mariano
We expand Äech cohomology of a topological space with values in a presheaf on to Äech cohomology of a commutative ring with unity with values in a presheaf on . Th…
math.CT2024
Grothendieck prelopologies: towards a closed monoidal sheaf category
Ana Luiza Tenório, Hugo Luiz Mariano
In this paper, we present a generalization of Grothendieck pretopologies -- suited for semicartesian categories with equalizers -- leading to a closed monoidal category of shea…