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math.CT2026
Classifying localizing subcategories of a locally coherent category
Reza Sazeedeh
Let $\cA$ be a locally coherent Grothendieck category, $\fp\cA$ be the full subcategory of $\cA$ consisting of finitely presented objects and $\ASpec\cA$ be the atom spectrum of $\…
math.CT2026
A new dimension for Grothendieck categories via the atom spectrum
Negar Alipour, Reza Sazeedeh
In this paper, we define a new dimension for objects in a Grothendieck category . We show that it serves as a lower bound for Gabriel-Krull dimension and under certain…
math.CT2025
Spectrum of an abelian category via premonoform objects
Reza Sazeedeh
Let $\cA$ be an abelian category. In this paper, we study ${\rm (n)PSpec}\cA$, a topological space formed by equivalence classes derived from an equivalence relation on (noetherian…