3 papers
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…
math.CT2024
Expanding Čech cohomology for quantales
Ana Luiza Tenório, Peter Arndt, Hugo Luiz Mariano
We expand Čech cohomology of a topological space with values in a presheaf on to Čech cohomology of a commutative ring with unity with values in a presheaf on . The…
math.CT2023
Geometric contexts and applications to logic
Mayk de Andrade, Hugo Mariano
There are many examples of dualities between topological spaces and algebras in the literature. Particularly, many of those examples come from the algebraic counterpart of a logica…