The authors prove that pointed matroids over perfect idylls form a combinatorial proto-exact category with duality and exact direct sum, and that tropical toric reflexive sheaves (modular ones in particular) are proto-exact and proto-abelian, with Khan-Maclagan Harder-Narasimhan filtrations realized
Axioms for infinite matroids
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Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves
The authors prove that pointed matroids over perfect idylls form a combinatorial proto-exact category with duality and exact direct sum, and that tropical toric reflexive sheaves (modular ones in particular) are proto-exact and proto-abelian, with Khan-Maclagan Harder-Narasimhan filtrations realized