2024/10/08 by João Dias, Dias, João, Bruno Dinis +3
Environmental Science · #06B15 #13L05 #16S60 #16U90 #Commutative Algebra (math.AC) #FOS: Mathematics #Landslides and related hazards #Logic (math.LO) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2410.05921
openalex publication_date 2024/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We bridge sheaves of rings over a topological space with common meadows (algebraic structures where the inverse for multiplication is a total operation). More specifically, we show that the subclass of pre-meadows with a, coming from the lattice of open sets of a topological space X, and presheaves over X are the same structure. Furthermore, we provide a construction that, given a sheaf of rings F on X produces a common meadow as a disjoint union of elements of the form F(U) indexed over the open subsets of X. We also establish a correspondence between the process of going from a presheaf to a sheaf (called sheafification) and the process of going from a pre-meadow with a to a common meadow.