2025/09/09 by Jaiung Jun, Jun, Jaiung, Alex Sistko +3
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Category Theory (math.CT) #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2509.08144
openalex publication_date 2025/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the category F-Mat_\bullet of matroids over an idyll F. We show that F-Mat_\bullet is a proto-exact category, a non-additive generalization of an exact category by Dyckerhoff and Kapranov. We further show that F-Mat_\bullet is proto-abelian in the sense of André. As an application, we establish that the category TRS_\bulletΣ of tropical toric reflexive sheaves associated to a fan Σ, introduced by Khan and Maclagan, is also proto-exact and proto-abelian. We then investigate the stability of modular tropical toric reflexive sheaves within the framework of proto-abelian categories and reformulate Harder-Narasimhan filtrations in this setting.